What about the men, though? Relative wage opportunities and the persistence of employment gaps in couples

Hammer, Luisa Working Paper What about the men, though? Relative wage opportunities and the persistence of employment gaps in couples IAB-Discussion Paper, No. 01/2025 Provided in Cooperation with: Institute for Employment Research (IAB) Suggested Citation: Hammer, Luisa (2025) : What about the men, though? Relative wage opportunities and the persistence of employment gaps in couples, IAB-Discussion Paper, No. 01/2025, Institut für Arbeitsmarktund Berufsforschung (IAB), Nürnberg, https://doi.org/10.48720/IAB.DP.2501 This Version is available at: https://hdl.handle.net/10419/313020 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Relative wage opportunities and the persistence of employment gaps in couples Luisa Hammer ISSN 2195‑2663 What about the men, though? Relative wage opportunities and the persistence of employment gaps in couples Luisa Hammer (IAB und Freie Universität Berlin) Mit der Reihe „IAB‑Discussion Paper“ will das Forschungsinstitut der Bundesagentur für Arbeit den Dialog mit der externen Wissenschaft intensivieren. Durch die rasche Verbreitung von Forschungsergebnissen über das Internet soll noch vor Drucklegung Kritik angeregt und Qualität gesichert werden. The “IAB‑Discussion Paper” is published by the research institute of the German Federal Employment Agency in order to intensify the dialogue with the scientific community. The prompt publication of the latest research results via the internet intends to stimulate criticism and to ensure research quality at an early stage before printing. Contents 1 Introduction...............................................................................6 2 Data .......................................................................................9 2.1 Samples.................................................................................. 10 3 Background: Gender Inequality in Germany......................................... 11 4 Methods ................................................................................. 14 4.1 Shift‑share approach ................................................................... 15 4.2 Estimation strategy ..................................................................... 19 5 Results .................................................................................. 21 6 Potential mechanisms ................................................................. 25 6.1 Household‑specialization according to Gary S. Becker ........................... 25 6.2 Equalizing wages ....................................................................... 27 6.2.1 Household productivity ....................................................... 27 6.2.2 Gender‑specific preferences for the household good .................... 27 6.2.3 Gender‑specific preferences and norms for market work ............... 28 7 Heterogeneity Analyses and Robustness ............................................. 31 7.1 Robustness .............................................................................. 31 7.2 Which pattern do the effects follow? ................................................ 32 7.3 Corroboration of results using observed couples’ relative incomes ............ 33 7.4 Further heterogeneity analyses....................................................... 33 7.5 What about the singles?............................................................... 34 7.6 Selection into partnership............................................................. 35 8 Conclusion .............................................................................. 35 References...................................................................................... 37 Appendix .................................................................................... 42 IAB‑Discussion Paper 01|2025 3 Abstract Gender gaps in employment have narrowed but remain substantial, particularly among couples. To estimate how improved female wage opportunities influence partners’ employment choices, I exploit demand‑driven wage changes in job tasks and German administrative data. Results indicate women respond positively, albeit at a diminishing rate, to relative wage improvements, while male partners also increase their labor supply in response. Consequently, the work hours gap within couples narrows, but doesn’t close and even widens in certain groups. Potential explanations for these patterns building on Becker’s household model include comparative advantages for women, and relative income preferences and gender identity norms for men. Zusammenfassung Die geschlechtsspezifischen Unterschiede bei der Beschäftigung haben sich verringert, sind aber nach wie vor beträchtlich, insbesondere innerhalb von Paaren. Um abzuschätzen, wie sich verbesserte Lohnmöglichkeiten für Frauen auf die Beschäftigungs‑ entscheidungen der Partner auswirken, nutze ich nachfragegesteuerte Lohnveränderungen bei Arbeitsaufgaben und deutsche Verwaltungsdaten. Die Ergebnisse deuten darauf hin, dass Frauen positiv, wenn auch mit abnehmender Tendenz, auf relative Lohnverbesserungen reagieren, während männliche Partner als Reaktion darauf ebenfalls ihr Arbeitsangebot erhöhen. Infolgedessen verringert sich die Arbeitszeitlücke innerhalb von Paaren, schließt sich aber nicht und vergrößert sich in bestimmten Gruppen sogar. Mögliche Erklärungen für diese Muster, die auf Beckers Haushaltsmodell aufbauen, sind komparative Vorteile für Frauen sowie relative Einkommenspräferenzen und Geschlechtsidentitätsnormen für Männer. JEL D13, E32, J12, J16, J22 IAB‑Discussion Paper 01|2025 4 Keywords Gender pay gap, female employment, household specialization, structural change Acknowledgements I would like to thank Alessandra Casarico, Natalia Danzer, Peter Haan, Nikolaj A. Harmon, Matthias Hertweck, Jonas Jessen, Ulrich Schneider and Luca Stella for valuable feedback as well as participants at the 2022 meeting of the Society of the Economics of the Household (SEHO), University College London; the 2022 Spring Meeting of Young Economists, Orleans; the Vereinstagung für Socialpolitik (VfS) annual meeting 2022, the Workshop on Interactions between Labor and Marriage, Aarhus University; the 1st Berlin Workshop on Empirical Public Economics, Freie Universität Berlin, the BeNA Winter Workshop 2023, the IAB workshop ”Social Inequalities”, the 3rd Workshop on Gender and Economics, Luxembourg Institute of Socio‑Economic Research (LISER), the 3rd International Workshop on Migration and Family Economics, School of Management (IESEG) Paris, the Family and Gender Economics Study Group (GEFAM) workshop 2024 at Insper Sao Paulo and at the European Association of Labor Economists (EALE) 2024 for extensive comments and suggestions. An early version of this paper was prepared in collaboration with Astrid Pape. I thank her very much for her contribution to this project. IAB‑Discussion Paper 01|2025 5 1 Introduction Recent decades have seen improvements in female labor market outcomes and narrowing gender pay gaps, yet disparities persist (Blau/Kahn, 2007; Goldin/Katz, 2002; Olivetti/Petrongolo, 2016). Reasons for these gender differences are manifold. In particular, the disproportionate reward of working long hours appears to be one of the main drivers of the persistent gender pay gaps (Goldin, 2014). Further factors are the arrival of children (Kleven/Landais/Søgaard, 2019), the scarcity of affordable substitutes to household production (Cortes/Pan, 2013) or sticky gender roles attitudes (Fortin, 2005). Germany is one of the OECD countries with above‑average gender wage gaps (Kunze, 2018) and large gender employment differences: On average, men work 10.7 hours more in the labor market per week (32 percent) than women.1 Within couples, the gap is even larger with 13.5 hours (39 percent).2 This also translates into very large earnings differentials between partners – Men’s monthly net earnings are on average 1,265 euro3 (54%) higher than those of the female partner. At least since the seminal theory of the family by Becker (1973, 1981), it is well‑established that it is economically rational for spouses to specialize in the household or in the market according to their comparative advantage, which is mainly determined by spouses’ (potential) labor market earnings. Thus, in times when gender wage inequality is very high, (full) household specialization can be utility maximizing. However, as women’s wages relative to those of men increase, Becker’s model predicts a decrease of the degree of household specialization within partnerships, and hence a decline of the gender gap in market working hours.4 There is plenty of research showing that the relative economic stature of men has suffered in recent years. On the one hand, women benefit from task‑biased technological change (Black/Spitz‑Oener, 2010; Beaudry/Lewis, 2014) and from structural changes such as the expansion of the service sector (Rendall, 2018). Men, on the other hand, are penalized more by negative labor demand shocks, for example through Chinese import competition (Autor/Dorn/Hanson, 2018), or the degree of local robot penetration (Anelli/Giuntella/Stella, 2024). This raises the question as of why gender gaps in employment are so persistent even though women’s relative employment opportunities have improved. Given the predictions of a Beckerian household model, this study aims to investigate the relationship between male and female wage potentials and their impact on labor supply 1 Average between 2005 and 2019. Source: German Microcensus 2005‑2019. 2 Conditional on employment, the gender gap in weekly work hours is 9.4 hours (23 percent) and within couples 12.3 hours (26 percent). 3 In prices of 2015. 4 Assuming that relative household productivities are unchanged. IAB‑Discussion Paper 01|2025 6 and gender employment gaps within couples, with a focus on why gender gaps persist despite improving female employment opportunities. Germany presents an interesting case as it has significant regional differences in terms of male and female employment patterns, gender attitudes, wages and earning potentials. This is largely due to the division of Germany between 1949 and 1990, which created different economic incentives, but also opposing institutions and normative values (Boelmann/Raute/Schonberg, 2021; Campa/Serafinelli, 2019; Lippmann/Georgieff/Senik, 2020). By focusing on partnered men and women, one of the groups with the largest gender gaps, this paper contributes to the understanding of the dynamics of gender inequality in employment. Since I am interested in the slowing down of the closing of the gender employment gaps, I estimate linear and quadratic effects of the relative female‑to‑male wage to capture possible non‑linearities. As wages are only observed for a selected subset of persons who are employed, I construct an exogenous measure of potential wages of all men and women using a Bartik‑type instrument (Aizer, 2010; Bertrand/Kamenica/Pan, 2015; Shenhav, 2021). Traditionally, this combines the differential wage growth across industries with the regional segregation of men and women in different segments of the labor market. Additionally, I exploit that task‑biased technological change favors women, leading to higher wage growth in female‑dominated tasks (Black/Spitz‑Oener, 2010). I therefore make a methodological contribution to the shift‑share approach and account for the role of tasks within industries. I show that there is substantial variation in the wage growth by task level within industries and that women and men specialize in different tasks within industries. The constructed relative potential wage then serves as an indicator of women’s wage opportunities relative to those of men in a standard full‑time employment. I also show that predicting gender wages exploiting the industry composition only yields very similar predictions for men and women, and thus a relative wage close to 100 percent since it neglects an important part of the within‑industry variation in wages. A further advantage of my paper is that I use high‑quality German administrative data for the wage measures. The results show that for women who live in a partnership, an increase of their earnings potential relative to those of the partner by one percentage point increases their hours of paid work conditional on employment on average by 0.17 hours, i.e. by 10 minutes. The positive effect becomes, however, significantly smaller, the higher the level of the relative potential wage. This suggests that while improving female earning potentials may incentivize greater labor force participation among women, the impact becomes less pronounced at higher levels of relative wage equality. Interestingly, men also increase their labor supply in response to relative improvements of their partner’s earning potentials, particularly when partnered with highly educated women. The quadratic decomposition suggests, however, that at low levels of the relative wage men’s work hours decrease, but the negative effect vanishes at higher levels of the relative wage. Given both adjustments, the within‑couple employment gap narrows, but again at a diminishing rate. On average, IAB‑Discussion Paper 01|2025 7 the gap remains unaffected, and therefore does not close. In some groups, it even widens significantly. So even if a woman could potentially contribute a high income to the family, the within‑couple gap in working hours does not close further. Still, women’s incomes rise slightly, whereas men’s incomes are unaffected (despite their increase in work hours). Yet, the share a woman contributes to the couple’s income increases only at a diminishing rate, which is, again, on average insignificant. Therefore, also the share of couples in which the woman is the secondary earner does not decline. Altogether, the findings suggest that the more advanced women’s integration into the labor market is, the lower the elasticity of female labor supply to changes in the relative wage, at least on the intensive margin. Men, on the other hand, appear to counteract their female partner’s improving earning opportunities. Understanding these mechanisms is particularly relevant for policy and taxation since it implies that public policies focusing on labor market returns only have little scope to increase female labor supply further and to reduce gender employment and earning gaps. The findings on diminishing effects align well with predictions from a Beckerian household model. The reversal of the effects at high levels of gender wage inequality, in particular for men, can only be reconciled with the model if preferences for the own earnings are endogenously formed and depend on the relative wage within couples as was acknowledged for instance by Bertrand (2020), Lundberg (2023) or Cortés/Pan (2023). Such preferences arise, and can in particular change, because of a wish to comply with social categories (Akerlof/Kranton, 2000) such as a ”traditional” division of market and household work in a couple. In sum, I contribute to the literature studying the link between relative female labor market opportunities (e.g., Autor/Dorn/Hanson, 2018; Kearney/Wilson, 2018; Anelli/Giuntella/Stella, 2024), especially of the relative female wage (e.g Shafer, 2011), and female employment. Close to my approach is Shenhav (2021) who estimates the effects of the relative female wage on marriage and total female employment. I add to this by specifically investigating whether the effects of improving relative female wage opportunities are non‑linear, and thus more relevant in very gender unequal societies, and by focusing on the group of partnered men and women – the group with the highest gender gaps in employment. Already Huber/Winkler (2019) and Halla/Schmieder/Weber (2020) showed that taking into account the household perspective has important implications when estimating the effects of labor market shocks. My discussion on potential mechanisms further contributes to the literature investigating the impact of gender norms on behavior within couples, especially with respect to the male main‑earner norm which affects marital stability and employment choices in couples (e.g., Bertrand/Kamenica/Pan, 2015; Lippmann/Georgieff/Senik, 2020; West/Zimmerman, 1987). IAB‑Discussion Paper 01|2025 8 4.1 Shift-share approach I define the local labor market by state s17 and education level of each partner ep 18, and year t. The observed relative wage in each local labor market is likely correlated with state‑ or education‑specific characteristics and the outcome variables themselves. Another problem is that it is only observed for working persons. Therefore, I use a Bartik (1991) type shift‑share approach, which exploits labor demand changes across different labor market segments and gender segregation in the labor market, to predict female and male wages in a local labor market. This approach is a popular tool for the estimation of gender‑specific wages to reflect gender‑specific labor demand changes and not other potentially endogenous characteristics (Aizer, 2010; Bertrand/Kamenica/Pan, 2015; Katz/Murphy, 1992). It exploits that, historically, men and women tend to work in different industries and that the gender‑specific industry composition differs by state. The local gender‑specific employment share in industry j19 (share) in a sufficiently lagged base year t0 is then multiplied with national wage changes by industry (shift). As base year I pool the years 1995 and 1996 in the Microcensus. I choose a base year t0 that is sufficiently distant to the estimation period 2005 to 2019 but which is also not too close to the drastic economic restructuring after German reunification (Hunt, 2001). The wage shifts are measured in the SIAB as the national average excluding the state in which the individual resides wjt,−s. This alleviates concerns of finite sample bias which arises if one included the own local observations (Goldsmith‑Pinkham/Sorkin/Swift, 2020). A nation‑wide change in industry‑specific wages hence impacts regions very differently, depending on the historical gender‑specific industry employment. Figure A4 in the Appendix illustrates the industry composition in the base years 1995 and 1996 by gender. There is, for example, a substantially higher share of men working in the production sector. Women, on the other hand, are concentrated in the sectors retail, education and health. Given the observed labor demand changes, the predicted wage is, thus, a measure of the potential wage in a standard full‑time employment. The potential wage wˆesgt per gender g and education group e in state s in year t is then given as: ∑ Ejesg,t0 wˆesgt = × wjt,−s (1) j Eesg,t0 17 I group the 16 German states into 13 states to account for small population size (Schleswig‑Holstein & Hamburg, Lower Saxony & Bremen, North‑Rhine‑Westphalia, Hesse, Rhineland‑Palatinate & Saarland, Baden‑Wuerttemberg, Bavaria, Berlin, Brandenburg, Mecklenburg‑Vorpommern, Saxony, Saxony‑Anhalt, and Thuringia). Unfortunately, the SUF of the Microcensus does not provide regional data on a more granular level. 18 I distinguish three education categories: no tertiary education, vocational training, and academic education. For the description of the shift‑share method, I will abbreviate ep as e. 19 I distinguish 13 industries based on Klassifikation der Wirtschaftszweige (WZ 93) displayed in Table A2. IAB‑Discussion Paper 01|2025 15 I then calculate the relative wage as the ratio between the predicted female wage and the predicted male wage. Figure 1: Gender Segregation by Task within Industries Women Men 0 .2 .4 .6 .8 1 Other public / private services Health Education Public service Real estate, housing, econ. serv Finance and insurance Information / communication Hospitality Retail, maintenance, repair Construction Energy / water supply Production Agriculture, forestry, fishing, 0 .2 .4 .6 .8 1 Other public / private services Health Education Public service Real estate, housing, econ. serv Finance and insurance Information / communication Hospitality Retail, maintenance, repair Construction Energy / water supply Production Agriculture, forestry, fishing, Notes: This figure shows the main task composition within industries by gen‑ der in the base years 1995 and 1996. Source: Own calculations based on Microcensus 1995/96 and BIBB 1998/99. Accounting for the role of tasks IAB‑Discussion Paper 01|2025 16 Aggregate wage growth does not only vary by industry, but it also varies substantially within industries by task level and their different exposure to technological change. According to the hypothesis of task‑biased technological change, non‑routine tasks are not easy to replace by modern technology and benefit from above‑average wage growth. For Germany, Black/Spitz‑Oener (2010) show that men and women were differentially affected by these adjustments. As women are over‑represented in non‑routine analytical and interactive tasks, task‑biased technological change benefited women, which eventually supported the catching‑up of female wages. In order to capture this variation, I identify the main task per occupation code KLDB 1988 using the Qualification and Career Survey carried out by the German Federal Institute for Vocational Training (compare 2). The dataset includes information on the activities regularly performed by employees on the job. I use data from the survey carried out in 1998 and 1999 which covers 30,000 respondents. In line with Black/Spitz‑Oener (2010), I assign each activity to one of five categories (non‑routine analytical, non‑routine interactive, routine cognitive, routine manual, and non‑routine manual) as defined in Table A3 and calculate the main task of each occupation. This classification is then added to both the German Microcensus and the SIAB which allows the construction of industry‑task cells. Figure 2: Wage Growth by Task in the Two Largest Industries Production Retail, maintenance 60 80 100 120 140 160 180 200 Daily wage (€) 1995 2000 2005 2010 2015 2020 60 80 100 120 140 160 180 200 Daily wage (€) 1995 2000 2005 2010 2015 2020 Notes: This figure plots the average imputed observed wage by task within the two largest industries. In prices of 2015. Source: Own calculations based on SIAB 1995–2016 and BIBB 1998/99. ∑ E jesg,t 0 ∑ E ojesg,t 0 wˆ esgt = × × w ojt,−s (2) j E esg,t 0 o E jesg,t 0 where E measures the total employment per group jesg in base year t 0 . 20 In the Appendix in Figure A5, I plot wages by task for all industries. 21 Shenhav (2021) expanded the original approach by Bertrand/Kamenica/Pan (2015) and included occupations within industries as an additional layer. As was shown by Black/Spitz‑Oener (2010), in particular the role of job tasks explain a substantial share of the closing of the gender gap. Therefore, I focus on the main tasks performed per occupation within industry instead. IAB‑Discussion Paper 01|2025 17 Figure 1 visualizes how the distribution of main tasks varies by gender within the 13 industries. For women, the share of non‑routine interactive tasks is substantially higher. This alone, however, does not make my approach superior to using industry variation only. It additionally requires that average wages vary by task within industries. In Figure 2, I show that wage growth differs strongly by tasks within the two largest industries. In production, the most important industry for men, women are over‑represented in the most productive tasks – non‑routine analytical and non‑routine interactive. In the retail sector, the picture is similar as women here disproportionally benefit from the high wages in non‑routine analytical tasks. The standard approach uses only the industry‑wide average wages, neglecting wage dispersion by task. I, on the other hand, exploit wage shifts by occupation task o within industries j and also consider the initial industry‑task employment compositions. The potential wage is then given as 21 20 The first sum captures the between‑industry exposure, the second sum captures the within‑industry exposure generated through the task composition within industries in the base year. For men and women, I predict their potential wage based on education group, state and year. The relative wage is then given by the ratio between the female and the male prediction. As a result, predicted relative wages vary over the 13 states s, 3 female education groups ew, 3 male education groups em and year t: wˆewst,fem \ = (3)RP W em,ew,s,t wˆemst,men Identifying assumptions IAB‑Discussion Paper 01|2025 18 In this set‑up, the variation in the shift‑share wages comes from the employment shares per industry‑task combination which vary by gender, region, and education group. Interacted with national wage shifts, this generates a differential exposure to a common wage shock – implying that differential exposure leads to differential changes in the outcome. To better understand where the variation in the identification strategy stems from, I calculate the annual Rotemberg weights per industry‑task cell as suggested in Goldsmith‑Pinkham/Sorkin/Swift (2020). The authors show that the Bartik estimator essentially implies using local employment shares as instruments, and so the exclusion restriction should be interpreted in terms of the shares. The Rotemberg weights (Rotemberg, 1983) measure the importance of each industry‑task employment share as an instrument in the overall shift‑share estimator. Even though I do not use the predicted Bartik wages in an instrumental variable estimation, I follow the argumentation of Goldsmith‑Pinkham/Sorkin/Swift (2020) and investigate the exogeneity conditions in terms I plot the predicted relative wage in Figure A6 in the Appendix by education‑match group for the estimation period (2005‑2019). The overall pattern follows the upward trend of the observed relative wage. As I am only considering the variation induced through the changes in labor demand of the total variation in male and female wages, the predicted relative wage is higher than the observed relative wage. Using my task‑industry shift‑share instrument the predicted relative wage on average amounts to 98.3 percent. When I predict the relative wage exploiting only the industry segregation the average size is 99.9 percent. Using the industry variation only predicts pretty similar wages for men and women as a crucial part of the wage variation within industries is neglected (compare Figure 2). Overall, the correlation between the predicted daily wage using the task‑industry shift‑share (the industry shift‑share) and the observed net incomes in the Microcensus data amounts for the female wage to 27 percent (16 percent) , for the male wage to 27 percent (12 percent), and for the relative wage to 10 percent (10 percent). 4.2 Estimation strategy The goal of the study is to test how a rising relative potential wage affects partner’s employment. Specifically, I investigate whether it affects them linearly, or whether the effects become smaller or larger at a higher level of the relative wage. The outcomes of interest can be grouped into two main categories: (1) employment outcomes of female partners and their male partner and (2) within‑couple employment differences. (1) comprises an indicator for employment participation, the number of weekly working hours IAB‑Discussion Paper 01|2025 19 Additionally, I test for significant pre‑trends in table A5. To do so, I replicate the regressions outlined in chapter 4.2 for the main outcomes measured in the years 1997 to 2004. As as a measure of exposure to the growth in the relative wage, I use the difference in the predicted relative wage between 2019 and 2005. For women and the important work hours outcomes, the estimates are all insignificant. Only for the employment of male partners, the results suggest that male partners that were exposed to higher growth rates of the relative wages in the 2000s had lower employment rates in the years 1997 to 2004. But the results point to no significant pretrends. of the shares, but focus the attention to those shares with the largest Rotemberg weights. I find that over the estimation period the most important industry‑task combinations are non‑routine interactive tasks in the real estate, production and health sectors for women and non‑routine interactive tasks in the education and production industry as well as routine cognitive tasks in the production sector for men. It would be worrisome if the estimated effects only reflect that time‑trends were very different in these industry‑task cells. In a robustness check, I therefore show that the results remain essentially unchanged when I exclude these industry‑task combinations, and when controlling for specific time trends across areas with different initial employment shares in the industry‑task cells with largest Rotemberg weights as suggested in Anelli/Giuntella/Stella (2024). I assess whether the employment shares correlate with other variables in the base year which could affect the outcomes directly, and irrespective of the shifts. Therefore, I analyze the correlation of the industry‑task shares with the share of persons with non‑German citizenship, the female share, the level of urbanization, and the average age per education‑state‑cell. I show in Table A4 for the three industry‑task combinations with the largest Rotemberg weights that some of these characteristics and the employment shares are indeed correlated, especially for men. However once I include education and state fixed effects, almost all covariates become insignificant. Nevertheless, I decide to not only use a wide set of fixed effects in the final regressions, which should absorb partly these correlations, but I also add the correlated variables as time‑varying control variables. and weekly working hours conditional on employment.22 The former measure of working hours codes working hours in case of non‑participation as zeros and hence combines participation margin and intensive margin, whereas conditional working hours measure only the pure intensive margin. (2) measures the difference between the man’s and the woman’s work hours and the percentage gap. The gaps are estimated for all couples as well as for dual‑earner couples, only. \ Yi = α1 + β1 RP W em,ew ,s,t + δ1,t + ϵ1,s + ζ1,s×t + η1,em×ew + θ1,em×ew ×s + ι1,iscw + (4) κ1,iscm + λ1,aw + µ1,am + ν1,agegap + π1,gap×matchtype + ρ1,q + σ1Xi + ω1,i \ 2 RP W Yi = α2 + β2 RP W em,ew,s,t + γ \ em,ew,s,t + δ2,t + ϵ2,s + ζ2,s×t + η2,em×ew + θ2,em×ew×s +ι2,iscw + κ2,iscm + λ2,aw + µ2,am + ν2,agegap + π2,gap×matchtype + ρ2,q + σ1Xi + ω2,i (5) The coefficient of interest β1 measures the average effect of an increase of the relative potential wage by one percentage point (pp). Coefficients β2 and γ do instead constitute the total marginal effect of the relative potential wage defined as d \ d Yi = β2 + 2 γ \ (6) RP W em,ew ,s,t RP W em,ew,s,t 22 Working hours are measured as the contractually agreed working hours. IAB‑Discussion Paper 01|2025 20 Apart from that I control for a number of fixed effects to absorb unobserved fixed differences, namely by year (δt), interview quarter (ρq), state (ϵs), state‑by‑year (ζs×t), θem×ew ×s for these education‑match‑state‑cells. It is important to note that the education‑match‑state‑cells which are used in the shift‑share approach may not only have different compositions of the local labor markets into industries and tasks, but might also differ in unobserved characteristics. To ensure that such unobserved differences are not falsely attributed to the predicted potential wages, I include fixed effects Hence, the marginal effect in Equation 6 depends on the size of , and, depending on the size and sign of γ, implies increasing, null or decreasing marginal effects. R \ P W em,ew ,s,t \ RP W em,ew ,s,t \ RP W em,ew ,s,t 2 \ RP W em,ew ,s,t I estimate two regressions: In Equation 4, I regress outcome Yi on the relative potential wage . In Equation 5, I regress outcome Yi of each couple i on the relative potential wage and the square of the relative potential wage . 5 Results In my preferred specification, I add a vector Xi which contains individual and couple control variables: being born in West Germany, partner being born in West Germany, being married, German nationality, partner has German nationality, living in an urban area, an indicator for having children aged 0 to 3 / 4 to 6 / 7 to 18 years living in the household, the total number of children under 18. Since the Microcensus dataset consists of repeated cross‑sections, I cannot include couple fixed effects. Standard errors ωi are clustered by state. Employment of female partners I find no significant effects of the relative potential wage on the participation margin of the female partners in panel A of Table 3, on average. The quadratic specification in column (2) shows, however, that the probability that female partners are employed increases significantly as their relative potential wage rises. Yet, this is offset by a reduction of the positive effect at higher levels of the relative wage. The total average effect as measured in column (1) is therefore a null effect. The same pattern is confirmed for working hours in column (3) and (4). Here, however, the total average effect is positive and significant at the 5 percent significance level. Conditional on employment of the woman, the average linear effect on working hours is statistically significant at the 1 percent level and positive: a rise of the relative potential wage by 1 percentage point (pp) raises the female partner’s work hours by 0.17 hours, i.e. 10 minutes. Applying the quadratic specification suggests again that the effect of a higher female‑to‑male potential wage is positive, but that it decreases 23 International Standard Classification of Education 97 (ISCED‑97) IAB‑Discussion Paper 01|2025 21 I begin by estimating Equation 4 and 5 to analyze the employment behavior of men and women who live in a cohabiting partnership. (ηem×ew ) of the woman (ιiscw ) and of the man (κiscm ) (λaw ) (µam ) education‑match , education indicator23 , age of the woman , and of the man , an indicator (νagegap) for whether the woman is more than 3 years older than the man, the man is more than 3 years older than the woman, or that they are roughly of the same age. I also allow for the age gap effects to differ by education match (πgap×matchtype). For example, couples in which the woman has a higher level of formal education, and is also older than the man, might respond very differently to the relative wage than ”standard” couples in which the man is at least as educated as the women and is at least around the same age. Table 3: Employment outcomes of partnered women and men Employed Working hours1 Cond. working hours2 Linear Quadratic Linear Quadratic Linear Quadratic (1) (2) (2) (4) (5) (6) Panel A: Female partners Rel. Potential Wage ‑0.001 0.037*** 0.189** 1.396*** 0.173*** 0.912** (0.003) (0.011) (0.089) (0.405) (0.044) (0.406) Rel. Wage × Rel. Wage ‑0.000*** ‑0.006*** ‑0.003* (0.000) (0.002) (0.002) Mean of the Dependent Var. 0.76 22.21 28.89 Standard Deviation 0.42 16.33 12.44 R2 0.17 0.17 0.26 0.26 0.23 0.23 Observations 995,583 995,583 995,583 995,583 765,987 765,987 Panel B: Male partners Rel. Potential Wage 0.006*** ‑0.009 0.380*** ‑0.730 0.144*** ‑0.410 (0.001) (0.013) (0.082) (0.682) (0.033) (0.295) Rel. Wage × Rel. Wage 0.000 0.005 0.003* (0.000) (0.003) (0.001) Mean of the Dependent Var. 0.92 38.34 41.4 Standard Deviation 0.25 13.72 8.86 R2 0.08 0.08 0.11 0.11 0.05 0.05 Observations 995,583 995,583 995,583 995,583 923,024 923,024 Notes: Regressions based on Equation 4 and 5. The sample includes women aged 22 to 55 and male partners aged 24‑57 years with non‑missing information on the relevant variables in the years 2005‑ 2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. 1 In case of non‑employment, working hours coded as zero. 2 Conditional on employment. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. significantly as the relative wage rises. This underlines that looking at the insignificant linear coefficient as in column (1) only can be misleading since it neglects what is happening along the distribution of relative wages. Employment of male partners I then investigate the employment behavior of the male partners in panel B of Table 3. The estimations show that a higher female‑to‑male wage potential also has significant effects on the employment of the male partners. An increase of the relative potential wage by 1 pp significantly increases the employment probability by 0.6 pp. The quadratic specification IAB‑Discussion Paper 01|2025 22 does not find significant effects. The relative wage also has a highly significant positive effect on the working hours of the male partners. This also holds when restricting on employed men, only. When decomposing the adjustments into a linear and a quadratic adjustments, the estimations suggest that at low levels of the relative wage, the male partners reduce their work hours if they are employed. At higher levels of the relative wage, their work hours do, however, on average rise. The positive adjustment of men’s work hours at high levels of the relative wage is significant at the 10 percent significance level. This positive adjustment appear to outweigh the reduction so that on average male work hours rise as the female partner’s earnings potential increases relative to that of the man.. Female vs. male effects Figure 3: Average marginal effects on work hours Women Men Notes: This figure shows the average marginal effects for different levels of the relative potential wage as de‑ fined in Eq. 6 using the quadratic specification from Eq. 5. The dependent variable measures the work hours conditional on employment. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005– 2019 and BIBB 1998/99. IAB‑Discussion Paper 01|2025 23 Figure 3 plots the average marginal effects defined in Eq. 6 along the distribution of relative wages. They are obtained using the quadratic regression from Eq. 5. It illustrates that the marginal effect of the relative wage on work hours for women stays significantly positive as long as the relative wage lies below 120 percent. For male partners, at low levels of the relative wage, the marginal effect is not significantly different from zero. But as soon, as it exceeds 100 percent the effect turns significantly positive. These patterns suggest that women at ”low” levels of the relative wage on average increase their work hours, but that the effects becomes increasingly smaller. Men, on the other hand, only start to react to the relative potential wage when it becomes ”too large”. Employment differences within partnerships Finally, I want to understand whether these individual employment patterns affect the degree of household specialization within couples. Therefore, I estimate the effect of a rising relative wage on the absolute differences between the working hours of the man and the woman in a partnership, and the hours difference relative to the male partner’s working hour, that is the hours gap in percent. In columns 1 to 4 of Table 4, I include all couples and in columns 5 to 8 only those couples in which both partners are employed. Table 4: Employment differences within partnerships Hours diff.1 Hours gap (%) Cond. hours diff.1 Cond. hours gap1 (%) Linear Quadratic Linear Quadratic Linear Quadratic Linear Quadratic (1) (2) (3) (4) (5) (6) (7) (8) Rel. Potential Wage 0.191* ‑2.126*** 0.000 ‑0.068*** ‑0.049 ‑1.499*** 0.001 ‑0.072*** (0.100) (0.677) (0.003) (0.016) (0.058) (0.434) (0.002) (0.022) Rel. Wage × Rel. Wage 0.011*** 0.000*** 0.007*** 0.000*** (0.003) (0.000) (0.002) (0.000) Mean of the Dep. Var. 16.1 0.41 12.8 0.24 Standard Deviation 20.2 0.67 14.9 0.67 R2 0.17 0.17 0.11 0.11 0.21 0.21 0.07 0.07 Observations 995,583 995,583 923,024 923,024 726,646 726,646 726,646 726,646 The results show that the relationship between the relative wage and the within‑couple working hours differences / gaps is highly non‑monotonic. The within‑couple difference in working hours declines significantly as the relative wage rises, but at a decreasing rate. The overall, average effect in column (1) suggests that as the potential wage of women relative to men increases by 1 pp, the within‑couple hours difference widens by 0.19 hours. Taking into consideration adjustments on the participation margin, the hours difference and percentage gap in dual‑earner couples are on average not affected (columns (5) and (7)). Yet again, the quadratic specifications show that indeed at lower levels of the relative wage the gap shrinks, but this negative effect becomes smaller as the relative wage rises, and in sum adds up to a null effect. The same pattern is found for the percentage hours gap. This means that in dual‑earner couples on average the hours gap does increase by 0.5 pp as the relative wage rises by 1 pp. Altogether, the estimations show that both partners appear to react non‑linearly to the relative potential wage. Surprisingly, the effects seem to be very important for the male IAB‑Discussion Paper 01|2025 24 Notes: Regressions based on Equation 4 and 5 for all women who live with their partner in the same household. The sample includes women aged 22 to 55 and male partners aged 24‑57 years with non‑missing information on the relevant variables in the years 2005‑2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 1 0.05, *** p < 0.01. Difference = average hours of the male partner minus average hours of the female partner; 2 Conditional on employment of both partners. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. 7 Heterogeneity Analyses and Robustness 7.1 Robustness First, I report the estimation results for specifications using different sets of fixed effects in table A9. The signs of the estimated coefficients if significant do not vary. In particular the results for the male partners and the couple gaps do not change upon using additional fixed effects. The estimations for the female partner’s intensive margin are slightly more sensitive. Then, I conduct multiple robustness checks to investigate the validity of the empirical approach and report results in Table A10. First, I test the sensitivity of the results to different model specifications. In panel B, I add indicators whether the female and male partners were employed in the previous year and whether their main ”occupation” was housewife / man to take into account path dependencies of the current decisions. The individual employment history has a high explanatory power. But the coefficients of the relative wage and their levels of significance is virtually unchanged. In panel c, I exclude the individual control variables such as children, foreign nationality, and being born in West Germany. Still, the main results remain robust. In panel D, I add dummies for the local annual decile of the relative earned household income to see whether economic necessity could explain the effects. Yet, the results remain virtually unchanged. Moreover, since the estimation results could be driven by the the sectors with the largest Rotemberg weights,27 I test whether the exclusion of these task‑industry cells affects the results in Panel E. The qualitative results remain the same. Only, for women the exclusion of these task‑industry cells seems to make a difference since without them the quadratic specification for work hours conditional on employment is now highly significant. Additionally, to further investigate the sensitivity of the shift‑share wage, I add time‑trends that differ across areas with different degrees of initial employment shares of these industry‑task combinations.28 Qualitative findings remain robust, yet, the level of significance increases. In the baseline estimation I use the current relative potential wage as explanatory variable. Since it is possible that the relative wage takes some time to affect partner’s employment decisions, in panel G, I show the results for using the relative wage lagged by one year as main explanatory variable. For the female partners, the lagged relative wage estimates that the level of significance for the quadratic effects on the work hours conditional on employment decreases. For the male partners, on the other hand, the level of significance of the quadratic effects on working hours increases so that the linear as well as the coefficient are 27 Compare section 4.1. 28 I construct the differential time trends by interacting year dummies with quartiles of the share of employment in these industry‑task combinations in the base year. IAB‑Discussion Paper 01|2025 31 significant at the 10 percent and 5 percent level respectively. Also, it finds that the within‑couple gaps widen for all couples as well as in dual‑earner couples significantly. In panel H, I additionally add the relative potential wage lagged by five years. The inclusion does not affect the estimated effects of the current relative wage very much. However, especially for the female partners the relative wage lagged by five years is an important explanatory factor, too. The estimated effects carry the same signs as those of the current relative wage. For men that earlier relative wage does not play a significant role. This points to the possibility that path dependencies play an important role for employment decisions. Reassuringly, the results remain robust to the various robustness analyses. My results provide robust evidence that the effect of an increasing relative female wage on employment choices in couples depends on the level of local gender equality in potential earnings. 7.2 Which pattern do the effects follow? In my baseline estimations, I investigate whether employment choices of partners react in a quadratic patterns towards changes in the relative potential wage. Now, I inspect further non‑linear specifications in table A11. When I measure the relative wage in logs in panel I, I find a significant positive effects of female work hours conditional on employment. Also the effects on the employment of male partners are significantly positive. The logarithmic specification thus suggests a positive but decreasing effect on male employment. It is hard to reconcile this result with economic theory. Also it seems rather to capture the same total average effect which is being estimate using the linear specification. Using a cubic instead of a linear or quadratic specification almost never yields significant results. An important exception are the working hours of the male partners conditional on employment. Here, the linear coefficient is significantly negative, the quadratic coefficient is positive, and the cubic coefficient is again negative. This suggests that male partners at the tails of the distribution again react differently. To inspect this more closely, I also run estimations investigating responses at different points of the relative wage in table A12. First, I check whether the response to the relative wage differs depending on whether the relative wage lies above the equal‑earning‑potential (compare section 6.2.3). For women, this makes no difference. For men, however, this point matters. If the relative potential wage amounts to at least 100 percent, male partner’s likelihood to be employed and work hours increase significantly. For those below, there is no effect. As a result, the within‑couple hours gap also only widens in couples with a relative wage above 100 percent. For these others, it closes significantly. IAB‑Discussion Paper 01|2025 32 7.3 Corroboration of results using observed couples' relative incomes So far, all estimations used the predicted ratios between female and male potential earnings as a measure of relative income opportunities in couples. Now, I want to corroborate the results using the observed relative incomes in couples in table A13. For the whole sample, the effects of the relative incomes in the couples is highly significant for all outcomes and all specifications. For women, all coefficients have the same signs as the regressions using the relative potential wage – there is a positive but diminishing effect of the relative income. For men, the estimations find that a higher relative female income is associated with fewer working hours. Therefore, on average, also the within‑couple hours gap is lower in couples with higher relative incomes. The positive, diminishing effects of the relative income on female partner’s employment and negative, but diminishing effects on male partner’s employment align well with my main results. They do, however, have several limitations. First of all, the relative income is a more meaningful measure in couples in which at least one partner, or ideally both are working. Moreover, the coefficients are very hard to interpret since the outcome variable, working hours, is also implicitly part of the variable of interest. Working hours constitute the labor market income. Lastly, the realized labor market incomes are driven by many other selection processes that are not addressed here and cannot be fully absorbed by the fixed effects. So these estimates simply measure associations, but are likely to also carry part of the underlying story. 7.4 Further heterogeneity analyses Generally, one of the most important determinants of female labor supply is motherhood. Female and male employment patterns and earnings suddenly start to diverge significantly after the birth of the first child (Kleven/Landais/Søgaard, 2019; Jessen, 2021). It is plausible that mothers are more responsive to changes in their relative earnings opportunities, particularly given their low baseline employment. Childless women, on the other hand, are less restricted in their labor supply and, thus, likely to have already adjusted to their individual optimal employment. To investigate whether the relative wage is more relevant in the presence of children, I perform a heterogeneity analysis in Table A17. The results show that indeed it is only mothers who experience a significant positive but diminishing effect of the relative wage. However, for their male partners the picture is reversed. Fathers react strongly linearly on improving female wage opportunities through longer work hours. Childless men, on the other hand, react in a convex pattern. As a result only the hours gap in couples with children widen. IAB‑Discussion Paper 01|2025 33 7.5 What about the singles? Becker’s theory of the household only predicts adjustment of partners in a marriage (or cohabiting partnership). In table A22, I investigate whether single women’s and men’s employment choices react to the relative potential wage29. And indeed, single women react similarly as partnered women with a positive but diminishing effect on improving relative wage opportunities. Also their labor incomes rise, on average, as their relative earnings opportunities improve. Single men’s employment choices, on the other hand, are not affected by the relative potential wage. Interestingly, however, their average labor incomes decreases significantly as relative female‑to‑male wage opportunities improve. That single women only ”reluctantly” increase their work hours could be driven by a desire to signal attractiveness as in Bursztyn/Fujiwara/Pallais (2017). 29 I measure the relative wage as the average relative wage given the own education level. IAB‑Discussion Paper 01|2025 34 I now want to see whether couples differ depending on whether their match is more standard or not. Therefore, I first look at couples who differ by the type of education match in table A20: couples in which the man has the higher level of formal education, both have the same level, or the woman has the higher level. The concave reaction of the female work hours are not relevant for any of the groups. For the male partners, the significant convex response is driven by more common types of matchings, i.e. by cases in which the man is either more or equally educated as the woman. Also, male work hours increase significantly only in couples in which the woman is either equally or higher qualified than the male partner. This relates very well to the results for female partners with a university degree in table A18 since among female partners who have a university degree (17 percent) more than a third (36 percent) has a higher level of formal education than the partner. Besides the differences in culture between East and West Germany investigated in Table A6 (in Section 6), couples might also differ in their responses to relative earnings opportunities given their level of education. In table A18 the results for a heterogeneity analysis by level of education of the female partner are displayed. For the woman’s employment, relative earnings opportunities only matter for women with no tertiary degree. And in this case it increase labor supply on the extensive and intensive margin. For their male partners, it is especially the partners of very highly educated women that increase their only labor supply if the woman’s relative earnings opportunities improve. This is also the only group in which the within‑couple hours gap conditional on employment widens significantly. For the educational level of the male partner, the differences are not so pronounced (compare table A19). 7.6 Selection into partnership 8 Conclusion Over the past decades, female employment outcomes have improved and gender gaps in terms of earnings and employment narrowed. However, the convergence seems to have stalled, despite technological advances which tend to favor the skill set of women (Goldin/Katz, 2002). In this paper I analyze the effect of a higher relative female‑to‑male potential wage in Germany using different datasets from administrative sources. Taking into account the improving wage opportunities of women relative to men due to technological change, I find that the relationship between the relative wage and household specialization is non‑monotonic. While a higher relative wage increases female labor supply, the effect is diminishing as the relative wage rises and, on average, insignificant. Men, on the other hand, increase their labor supply on average, even though at low levels of the relative wage they decrease their work hours. In sum, this leads to a stagnation or even widening of the hours gap in couples as the relative wage rises, and also the probability that IAB‑Discussion Paper 01|2025 35 Lastly, selection into cohabiting partnerships may pose a problem to the estimation strategy since in that case I would not use a random sample. Therefore, I investigate the effect of the relative potential wage on the likelihood that a woman or a man is living in a cohabiting partnership in table A23. For women, a higher relative wage is significantly correlated with a higher likelihood to be living in a cohabiting relationship in the presence. For men only the probability to be married is significantly but negatively correlated to the relative wage. It is important to note, however, that the relative wage is measured in the current period, but the decision to move together with a partner was likely formed and realized years ago. This limits the meaningfulness of these results. Table A24 displays the characteristics of men and women by partnership status. Not surprisingly, women who do not live in a cohabiting partnership are younger, have less children, are more educated, are more active in the labor market and earn higher incomes than those women who are in cohabiting partnerships. Men who do not live in a cohabiting partnership are also younger. But the selection on employment seems to work in the opposite direction to those of women: ”single” men are less active on the labor market, earn lower incomes and are less educated than partnered men. Hence, the sample of partnered men and women is not generalizable to the overall population of men and women. Still, the estimations measure the effects of a rising relative potential female‑to‑male wage in cohabiting couples given their selection into a cohabiting partnership. a woman is not the secondary does not increase significantly. So female wage opportunities matter for women’s employment decision. But they also matter for men, so that the gaps do not close. This is particularly relevant for public policy aiming to improve female labor market outcomes by focusing on labor market return only. 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IAB‑Discussion Paper 01|2025 40 Wage growth by industry‑task combination cont. 60 80 100 120 140 160 180 200 Daily wage (€) 1995 2000 2005 2010 2015 2020 Non-rout. analytical Non-rout. interactive Rout. cognitive Rout. manual Non-rout. manual Industry average Information & communication 60 80 100 120 140 160 180 200 Daily wage (€) 1995 2000 2005 2010 2015 2020 Non-rout. analytical Non-rout. interactive Rout. cognitive Rout. manual Non-rout. manual Industry average Finance & insurance 60 80 100 120 140 160 180 200 Daily wage (€) 1995 2000 2005 2010 2015 2020 Non-rout. analytical Non-rout. interactive Rout. cognitive Rout. manual Non-rout. manual Industry average Real estate & housing, provision of econ. services 60 80 100 120 140 160 180 200 Daily wage (€) 1995 2000 2005 2010 2015 2020 Non-rout. analytical Non-rout. interactive Rout. cognitive Rout. manual Non-rout. manual Industry average Public service 60 80 100 120 140 160 180 200 Daily wage (€) 1995 2000 2005 2010 2015 2020 Non-rout. analytical Non-rout. interactive Rout. cognitive Rout. manual Non-rout. manual Industry average Education 60 80 100 120 140 160 180 200 Daily wage (€) 1995 2000 2005 2010 2015 2020 Non-rout. analytical Non-rout. interactive Rout. cognitive Rout. manual Non-rout. manual Industry average Health Notes: These figures plot the average imputed observed wage by task within industries. In prices of 2015. Source: Own calculations based on SIAB 1995–2019 and BIBB 1998/99. IAB‑Discussion Paper 01|2025 47 Wage growth by industry‑task combination cont. 60 80 100 120 140 160 180 200 Daily wage (€) 1995 2000 2005 2010 2015 2020 Non-rout. analytical Non-rout. interactive Rout. cognitive Rout. manual Non-rout. manual Industry average Provision of other public & private services Notes: These figures plot the average observed wage by task within industries. In prices of 2015. Source: Own calculations based on SIAB 1995–2019 and BIBB 1998/99. Figure A6: Predicted relative wage .7 .8 .9 1 1.1 1.2 Predicted relative wage 2005 2010 2015 2020 W No, M No W No, M Voc W No, M Uni W Voc, M No W Voc, M Voc W Voc, M Uni W Uni, M No W Uni, M Voc W Uni, M Uni Notes: This figure plots the average predicted relative wage based on eq. (2) separately by education‑match groups. No = no tertiary degree, Voc = voca‑ tional degree, Uni = Academic Degree; W = woman, M = man. Source: Own calculations based on Microcensus 1995/96, SIAB 2005–2019 and BIBB 1998/99. IAB‑Discussion Paper 01|2025 48 Table A1: Descriptive statistics Mean Minimum Maximum s.d. Female partners Age in years 40.56 22.00 55.00 8.61 No tertiary degree 0.14 0.00 1.00 0.35 Vocational degree 0.69 0.00 1.00 0.46 Academic degree 0.17 0.00 1.00 0.37 Employed 0.77 0.00 1.00 0.42 Number of hours working (normally) 22.21 0.00 98.00 16.34 Employed in the previous year 0.70 0.00 1.00 0.46 Housewife in the previous year 0.16 0.00 1.00 0.36 Real income 1118.17 0.00 2, 0881.67 1035.64 Observations 995,586 Male partners Age in years 43.14 24.00 57.00 8.54 No tertiary degree 0.10 0.00 1.00 0.30 Vocational degree 0.69 0.00 1.00 0.46 Academic degree 0.21 0.00 1.00 0.41 Employed 0.93 0.00 1.00 0.26 Number of hours working (normally) 38.35 0.00 98.00 13.72 Employed in the previous year 0.86 0.00 1.00 0.35 Houseman in the previous year 0.00 0.00 1.00 0.07 Real income 2,479.47 0.00 20881.67 1814.75 Observations 995,586 Couple households Age difference (man ‑ woman) 2.58 ‑30.00 34.00 4.25 Both around same age (+/‑3) 0.60 0.00 1.00 0.49 Man at least 4 years older 0.35 0.00 1.00 0.48 Man at least 4 years younger 0.05 0.00 1.00 0.22 Both have same level of education 0.73 0.00 1.00 0.44 Man has higher degree of education 0.17 0.00 1.00 0.38 Woman has higher degree of education 0.10 0.00 1.00 0.29 At least 1 child aged 0‑3 living in household 0.18 0.00 1.00 0.38 At least 1 child aged 4‑6 living in household 0.09 0.00 1.00 0.29 At least 1 child aged 7‑18 living in household 0.31 0.00 1.00 0.46 Number of children in household 0.99 0.00 12.00 1.04 Married 0.82 0.00 1.00 0.38 West Germany 0.81 0.00 1.00 0.39 Real household income 3,604.10 0.00 20881.67 2260.60 Observations 995,586 Notes: The sample includes partnered women between 22‑55 years and with non‑missing in‑ formation on the relevant variables (education, state, partner info). Male partners are aged 24‑57 years. The means of the binary variables refer to the shares. Incomes in prices of 2015 ( e). Source: Own calculations based on Microcensus 2005–2019. IAB‑Discussion Paper 01|2025 49 Table A2: Definition of industries Industry name WZ 93 code Agriculture, forestry, fishery & mining 011‑051, 101‑145 Production 151‑372 Energy & water supply 401‑410 Construction 451‑455 Trade, maintenance, repair 501‑527 Hospitality 551‑555 Information & communication 601‑642 Finance & insurance 651‑672 Real estate & housing, provision of economic services 701‑748 Public service 751‑753, 990 Education 801‑804 Health 851‑853 Provision of other public & private services 900‑930, 950 Notes: Industry classification based on Klassifikation der Wirtschaft‑ szweige 93 (WZ 93). Source: Klassifikation der Wirtschaftszweige 93. Table A3: Definition of tasks Task measure Activities Non‑routine analytical Researching, analysing, designing, sketching Non‑routine interactive Negotiating, lobbying, coordinating, organising, teaching, training, selling, buying, advising customers, advertising Routine cognitive Calculating, bookkeeping, measuring length/weight/temperature Routine manual Operating or controlling machines, equipping machines Non‑routine manual Repairing or renovating houses/machines/vehicles, restoring art/monuments, serving or accommodating Notes: Task classification following Black/Spitz‑Oener (2010) based on the Qualification and Career Survey. Source: BIBB 1998/99 IAB‑Discussion Paper 01|2025 50 Table A4: Correlation between industry‑task shares and characteristics Female industry‑task cells with largest Rotemberg weights Real estate / non‑routine interactive Production / non‑routine interactive Health / non‑routine interactive Non‑German nat. 0.0003 ‑0.0013* ‑0.0007 (0.0004) (0.0007) (0.0007) Female share ‑0.0008*** 0.0001 ‑0.0012** (0.0003) (0.0005) (0.0005) Average age 0.0030 0.0013 0.0084*** (0.0018) (0.0031) (0.0031) Urban share ‑0.0001* 0.0002* ‑0.0000 (0.0001) (0.0001) (0.0001) R2 0.23 0.16 0.45 Observations 78 78 78 Male industry‑task cells with largest Rotemberg weights Education / non‑routine interactive Production / non‑routine interactive Production / routine cognitive Non‑German nat. 0.0054*** 0.0008* ‑0.0041** (0.0008) (0.0004) (0.0016) Female share ‑0.0057*** ‑0.0015*** 0.0026** (0.0006) (0.0003) (0.0012) Average age 0.0138*** 0.0061*** 0.0034 (0.0039) (0.0018) (0.0075) Urban share 0.0002 0.0002** 0.0009*** (0.0001) (0.0001) (0.0003) R2 0.63 0.52 0.24 Observations 78 78 78 Notes: This table reports the correlation between the shares of different industry‑task combina‑ tions in 1995 and 1996 with other characteristics in the same years. Non‑German nat.: share of persons with non‑German citizenship, Urban: share district size >= 100, 000 inhabitants. Each column uses as dependent variable the employment share of the indicated industry‑task cell.* p < 0.10, ** p < 0.05, *** p < 0.01. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. Table A5: Investigating pre‑trends Female partners Male partners Couples Employment Cond. Work hours Employment Cond. Work hours Hours gap Cond. Hours gap Relative wage exposure 0.019 ‑0.202 ‑0.027* 0.357 0.018 0.026 (0.021) (0.676) (0.014) (0.387) (0.084) (0.082) R2 0.00 ‑0.01 0.03 ‑0.00 ‑0.01 ‑0.01 Observations 144 144 144 144 144 144 Notes: The sample includes women aged 22 to 55 and male partners aged 24‑57 years with non‑missing information on the relevant variables in the years 1997–2004. The variable relative wage exposure measures the change in predicted relative wages from 2005 to 2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. Source: Own calculations based on Microcensus 1995/96 & 1997–2004 , SIAB 2005–2019 and BIBB 1998/99. IAB‑Discussion Paper 01|2025 51 Table A6: Heterogeneous effects by East vs. West Germany Female partners Male partners Couples Employment Cond. Work hours Employment Cond. Work hours Hours gap Cond. Hours gap East Germany Rel. Potential Wage 0.013*** 0.101* 0.358*** 0.223 0.016*** 0.050 0.239*** 0.782 ‑0.016*** ‑0.092* ‑0.009** ‑0.027 (0.002) (0.050) (0.072) (0.632) (0.002) (0.053) (0.075) (0.452) (0.005) (0.049) (0.004) (0.059) Rel. Wage × Rel. Wage ‑0.000* 0.001 ‑0.000 ‑0.002 0.000 0.000 (0.000) (0.003) (0.000) (0.002) (0.000) (0.000) West Germany Rel. Potential Wage ‑0.004 0.032*** 0.118** 1.123* 0.004*** ‑0.018** 0.134*** ‑0.658** 0.005* ‑0.077*** 0.004** ‑0.091*** (0.003) (0.010) (0.055) (0.611) (0.001) (0.008) (0.031) (0.274) (0.003) (0.015) (0.002) (0.018) Rel. Wage × Rel. Wage ‑0.000*** ‑0.005 0.000** 0.004*** 0.000*** 0.000*** (0.000) (0.003) (0.000) (0.001) (0.000) (0.000) Mean West 0.69 28.61 0.89 40.9 0.45 0.31 Mean East 0.72 33.61 0.82 40.35 0.28 0.17 R2 0.09 0.09 0.11 0.12 0.07 0.07 0.05 0.05 0.05 0.05 0.04 0.04 Observations 995,586 995,586 765,990 765,990 995,586 995,586 923,027 923,027 923,027 923,027 726,649 726,649 Table A7: Partners’ realized labor income Average net incomes Income shares: all couples Income shares: dual‑earner couples Woman’s labor income Man’s labor income Household income Woman’s income share Woman earns more1 Woman’s income share Woman earns more Linear Quadratic Linear Quadratic Linear Quadratic Linear Quadratic Linear Quadratic Linear Quadratic Linear Quadratic Rel. Potential Wage 10.331** ‑34.427 ‑4.108 ‑44.119 0.660 ‑5.075 ‑0.001 0.021*** 0.000 0.015 0.000 0.018*** 0.001 0.021* (3.662) (39.421) (8.201) (45.891) (15.193) (84.532) (0.001) (0.006) (0.001) (0.010) (0.001) (0.005) (0.001) (0.011) Rel. Wage × Rel. Wage 0.206 0.184 0.026 ‑0.000*** ‑0.000 ‑0.000*** ‑0.000* (0.177) (0.198) (0.332) (0.000) (0.000) (0.000) (0.000) Maximum 83.7 119.9 96.2 101.8 112.1 110.3 115.2 R2 0.23 0.23 0.09 0.09 0.21 0.21 0.08 0.08 0.22 0.22 0.26 0.26 0.24 0.24 Observations 947,791 947,791 947,791 947,791 827,032 827,032 827,032 827,032 965,445 965,445 953,162 953,162 995,583 995,583 Mean 1118.17 2479.47 3604.09 0.32 0.14 0.35 0.15 Table A8: Effects of gender‑specific potential wages Female partners Male partners Couples Employment Cond. Work hours Employment Cond. Work hours Hours gap Cond. Hours gap Female potential wage ‑0.003* 0.015*** 0.068* 0.686*** 0.001 0.009*** 0.033** 0.258*** 0.002 ‑0.020*** 0.001 ‑0.017*** (0.002) (0.005) (0.035) (0.117) (0.001) (0.002) (0.014) (0.059) (0.001) (0.005) (0.001) (0.006) Male potential wage 0.001 ‑0.011** ‑0.007 ‑0.206 ‑0.006*** 0.002 ‑0.121*** 0.350*** ‑0.003 0.028*** ‑0.005*** 0.026*** (0.001) (0.005) (0.044) (0.118) (0.001) (0.004) (0.018) (0.115) (0.002) (0.005) (0.002) (0.005) Fem. wage × fem. wage ‑0.000*** ‑0.002*** ‑0.000*** ‑0.001*** 0.000*** 0.000*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Male wage × male wage 0.000** 0.001 ‑0.000** ‑0.001*** ‑0.000*** ‑0.000*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) R2 0.17 0.17 0.23 0.23 0.08 0.08 0.05 0.05 0.11 0.11 0.07 0.07 Observations 995,583 995,583 765,987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 IAB‑Discussion Paper 01|2025 52 Notes: Regressions based on eq. 4 and 5. The sample includes women aged 22 to 55 and male partners aged 24‑57 years with non‑missing information on the relevant variables in the years 2005‑2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. The effects per group are measured by interacting a group dummy with the relative wage. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. Notes: Regressions based on eq. 4 and 5 for all women who live with their partner in the same household. The sample includes women aged 22 and 51 with non‑missing information on the relevant variables in the years 2005‑2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. Average net labor market incomes (real 2015 value). Woman’s share of total couple’s net income. 1 Woman earns more than 50% of total couple’s household labor income. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. Notes: Regressions based on eq. 4 and 5. The predicted wages are lagged by one year. The sample includes women aged 22 to 55 and male partners aged 24‑57 years with non‑missing information on the relevant variables in the years 2005‑2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. Table A9: Fixed effects specifications Female partners Male partners Couples Employment Cond. Work hours Employment Cond. Work hours Hours gap Cond. Hours gap Year, state, year × state Rel. Wage 0.006*** 0.020*** 0.179*** ‑0.146 ‑0.000*** ‑0.006* ‑0.058*** ‑0.624*** ‑0.010*** 0.001 ‑0.007*** 0.012* (0.001) (0.004) (0.015) (0.116) (0.000) (0.003) (0.004) (0.059) (0.001) (0.003) (0.000) (0.006) Rel. Wage × Rel. Wage ‑0.000*** 0.002** 0.000* 0.003*** ‑0.000*** ‑0.000*** (0.000) (0.001) (0.000) (0.000) (0.000) (0.000) R2 0.14 0.14 0.19 0.19 0.04 0.04 0.02 0.02 0.09 0.09 0.05 0.05 Observations 995,583 995,583 765,987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 Year, state, year × state, education‑match, education‑match × state Rel. Wage 0.000 0.028** 0.187*** 0.647 0.006*** ‑0.002 0.122*** ‑0.081 ‑0.003 ‑0.034** ‑0.002 ‑0.038 (0.002) (0.012) (0.040) (0.401) (0.001) (0.013) (0.035) (0.284) (0.003) (0.016) (0.002) (0.023) Rel. Wage × Rel. Wage ‑0.000** ‑0.002 0.000 0.001 0.000* 0.000 (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) R2 0.15 0.15 0.20 0.20 0.07 0.07 0.03 0.03 0.09 0.09 0.06 0.06 Observations 995,583 995,583 765,987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 Year, state, year × state, education‑match, education‑match × state, female age, male age Rel. Wage 0.000 0.033** 0.180*** 0.825* 0.006*** ‑0.000 0.122*** ‑0.081 ‑0.003 ‑0.039** ‑0.002 ‑0.042* (0.002) (0.012) (0.048) (0.413) (0.001) (0.013) (0.033) (0.284) (0.003) (0.017) (0.002) (0.023) Rel. Wage × Rel. Wage ‑0.000*** ‑0.003 0.000 0.001 0.000* 0.000 (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) R2 0.16 0.16 0.21 0.21 0.07 0.07 0.03 0.03 0.10 0.10 0.06 0.06 Observations 995,583 995,583 765,987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 Year, state, year × state, education‑match, education‑match × state, female age, male age, female ISCED, male ISCED Rel. Wage ‑0.001 0.037*** 0.175*** 0.922** 0.006*** ‑0.010 0.144*** ‑0.418 0.000 ‑0.069*** 0.001 ‑0.073*** (0.003) (0.011) (0.044) (0.402) (0.001) (0.013) (0.033) (0.295) (0.003) (0.016) (0.002) (0.022) Rel. Wage × Rel. Wage ‑0.000*** ‑0.003* 0.000 0.003* 0.000*** 0.000*** (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) R2 0.17 0.17 0.23 0.23 0.08 0.08 0.05 0.05 0.11 0.11 0.07 0.07 Observations 995,586 995,583 765,990 765,987 995,586 995,583 923,024 923,024 923,024 923,024 726,649 726,646 Year, state, year × state, education‑match, education‑match × state, female age, male age, female ISCED, male ISCED, female age × male age Rel. Wage ‑0.001 0.037*** 0.175*** 0.881* 0.006*** ‑0.009 0.146*** ‑0.400 0.000 ‑0.067*** 0.001 ‑0.071*** (0.003) (0.011) (0.044) (0.419) (0.001) (0.013) (0.033) (0.300) (0.003) (0.016) (0.002) (0.022) Rel. Wage × Rel. Wage ‑0.000*** ‑0.003 0.000 0.003* 0.000*** 0.000*** (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) R2 0.17 0.17 0.23 0.23 0.08 0.08 0.05 0.05 0.11 0.11 0.07 0.07 Observations 995,583 995,583 765,987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 Year, state, year × state, education‑match, education‑match × state, female age, male age, female ISCED, male ISCED, age gap category , age gap category × education gap Rel. Potential Wage ‑0.001 0.037*** 0.173*** 0.912** 0.006*** ‑0.009 0.144*** ‑0.410 0.000 ‑0.068*** 0.001 ‑0.072*** (0.003) (0.011) (0.044) (0.406) (0.001) (0.013) (0.033) (0.295) (0.003) (0.016) (0.002) (0.022) Rel. wage × Rel. Wage ‑0.000*** ‑0.003* 0.000 0.003* 0.000*** 0.000*** (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) R2 0.17 0.17 0.23 0.23 0.08 0.08 0.05 0.05 0.11 0.11 0.07 0.07 Observations 995,583 995,583 765,987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 Notes: Regressions based on eq. 4 and 5. Each regression also includes fixed effects for quarter of interview. The sample includes women aged 22 to 55 and male partners aged 24‑57 years with non‑missing information on the relevant variables in the years 2005‑2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. IAB‑Discussion Paper 01|2025 53 Table A10: Robustness checks Female partners Male partners Couples Employment Cond. Work hours Employment Cond. Work hours Hours gap Cond. Hours gap A. Baseline Rel. Potential Wage ‑0.001 0.037*** 0.173*** 0.912** 0.006*** ‑0.009 0.144*** ‑0.410 0.000 ‑0.068*** 0.001 ‑0.072*** (0.003) (0.011) (0.044) (0.406) (0.001) (0.013) (0.033) (0.295) (0.003) (0.016) (0.002) (0.022) Rel. wage × Rel. Wage ‑0.000*** ‑0.003* 0.000 0.003* 0.000*** 0.000*** (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) R2 0.17 0.17 0.23 0.23 0.08 0.08 0.05 0.05 0.11 0.11 0.07 0.07 Observations 995,583 995,583 765,987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 B. Employment history Rel. Potential Wage 0.001 0.033*** 0.168*** 0.979** 0.004*** 0.005 0.146*** ‑0.321 ‑0.001 ‑0.057*** 0.001 ‑0.067*** (0.001) (0.008) (0.049) (0.376) (0.001) (0.009) (0.032) (0.293) (0.002) (0.016) (0.002) (0.022) Rel. wage × Rel. Wage ‑0.000*** ‑0.004** ‑0.000 0.002 0.000*** 0.000** (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) R2 0.55 0.55 0.25 0.25 0.32 0.32 0.06 0.06 0.21 0.21 0.10 0.10 Observations 995,583 995,583 765,987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 C. No covariates Rel. Potential Wage ‑0.001 0.038*** 0.161** 0.842 0.007*** ‑0.008 0.152*** ‑0.409 0.001 ‑0.071*** 0.001 ‑0.070*** (0.003) (0.012) (0.061) (0.515) (0.001) (0.013) (0.032) (0.297) (0.003) (0.016) (0.002) (0.022) Rel. wage × Rel. Wage ‑0.000*** ‑0.003 0.000 0.003* 0.000*** 0.000*** (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) R2 0.09 0.09 0.11 0.11 0.07 0.07 0.05 0.05 0.05 0.05 0.04 0.04 Observations 995,586 995,586 765,990 765,990 995,586 995,586 923,027 923,027 923,027 923,027 726,649 726,649 D. Control for household income Rel. Potential Wage ‑0.002 0.043*** 0.173*** 1.071** 0.005** ‑0.006 0.148*** ‑0.342 0.000 ‑0.074*** 0.001 ‑0.073*** (0.003) (0.010) (0.057) (0.455) (0.002) (0.013) (0.029) (0.263) (0.003) (0.017) (0.002) (0.022) Rel. wage × Rel. Wage ‑0.000*** ‑0.004* 0.000 0.002* 0.000*** 0.000*** (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) R2 0.21 0.21 0.25 0.25 0.14 0.14 0.08 0.08 0.11 0.11 0.07 0.07 N 995583 995583 765987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 E. Without top‑3 Rotemberg weight industry‑task cells Rel. Potential Wage ‑0.003* 0.041*** 0.052 0.501 ‑0.001 ‑0.013* ‑0.029 ‑0.335 ‑0.000 ‑0.056*** ‑0.003** ‑0.048*** (0.001) (0.005) (0.044) (0.386) (0.000) (0.007) (0.019) (0.215) (0.001) (0.013) (0.001) (0.015) Rel. Wage × Rel. Wage ‑0.000*** ‑0.002 0.000* 0.001 0.000*** 0.000** (0.000) (0.001) (0.000) (0.001) (0.000) (0.000) R2 0.17 0.17 0.23 0.23 0.08 0.08 0.05 0.05 0.11 0.11 0.07 0.07 Observations 995,586 995,586 765,990 765,990 995,586 995,586 923,027 923,027 923,027 923,027 726,649 726,649 F. Rotemberg weight time‑trend Rel. Potential Wage ‑0.003 0.058*** 0.107 1.137** 0.008*** ‑0.020* 0.126*** ‑0.669** 0.002 ‑0.095*** 0.002 ‑0.087*** (0.003) (0.010) (0.067) (0.488) (0.002) (0.011) (0.038) (0.249) (0.003) (0.016) (0.002) (0.023) Rel. Wage × Rel. Wage ‑0.000*** ‑0.005** 0.000** 0.004*** 0.000*** 0.000*** (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) Observations 995,586 995,586 765,990 765,990 995,586 995,586 923,027 923,027 923,027 923,027 726,649 726,649 R2 0.17 0.17 0.23 0.23 0.08 0.08 0.05 0.05 0.11 0.11 0.07 0.07 G. Relative wage lagged by one year Lagged Rel. Potential Wage ‑0.002 0.027* ‑0.004 0.332 0.005*** ‑0.010 0.100*** ‑0.496* 0.005* ‑0.042*** 0.005* ‑0.047*** (0.002) (0.013) (0.045) (0.247) (0.002) (0.013) (0.027) (0.270) (0.003) (0.011) (0.003) (0.015) Lag Rel. Wage × Lag Rel. Wage ‑0.000** ‑0.002 0.000 0.003** 0.000*** 0.000*** (0.000) (0.001) (0.000) (0.001) (0.000) (0.000) Observations 995,583 995,583 765,987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 R2 0.17 0.17 0.23 0.23 0.08 0.08 0.05 0.05 0.11 0.11 0.07 0.07 H. Add lag of relative wage by 5 years Rel. Potential Wage 0.000 0.040*** 0.119 0.652 0.008*** 0.000 0.192*** ‑0.218 0.002 ‑0.060*** 0.004 ‑0.059** (0.003) (0.011) (0.072) (0.405) (0.002) (0.015) (0.029) (0.302) (0.004) (0.017) (0.003) (0.024) Rel. Wage × Rel. Wage ‑0.000*** ‑0.002 0.000 0.002 0.000*** 0.000** (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) Lag 5: Rel. Potential Wage 0.002 0.047*** ‑0.118* 0.375 0.005** 0.002 0.105*** 0.304 0.004* ‑0.040** 0.007*** ‑0.022 (0.002) (0.012) (0.057) (0.328) (0.002) (0.008) (0.030) (0.229) (0.002) (0.017) (0.002) (0.016) Lag 5: Rel. Wage × Rel. Wage ‑0.000*** ‑0.002 0.000 ‑0.001 0.000** 0.000 (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) Observations 995,583 995,583 765,987 765,987 995,583 995,583 923,024 923,024 923,024 923,024 726,646 726,646 R2 0.17 0.17 0.23 0.23 0.08 0.08 0.05 0.05 0.11 0.11 0.07 0.07 IAB‑Discussion Paper 01|2025 54 Notes: Regressions based on eq. 4 and 5. The sample includes women aged 22 and 51 with non‑missing information on the relevant variables in the years 2005‑2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019. Table A11: Non‑linear specifications Female partners Male partners Couples Employment Cond. Work hours Employment Cond. Work hours Hours gap Cond. Hours gap Log of relative wage Log Rel. Potential Wage 0.014 20.278*** 0.604*** 13.681*** ‑0.140 ‑0.082 (0.268) (4.949) (0.167) (3.789) (0.281) (0.192) Observations 995,583 765,987 995,583 923,024 923,024 726,646 R2 0.17 0.23 0.08 0.05 0.11 0.07 Cubic specification Rel. Potential Wage 0.017 1.348 ‑0.145 ‑4.295** ‑0.192 ‑0.324* (0.090) (4.395) (0.093) (1.952) (0.148) (0.167) Rel. Wage × Rel. Wage 0.000 ‑0.008 0.001 0.041** 0.002 0.003 (0.001) (0.042) (0.001) (0.019) (0.001) (0.002) Rel. Wage × Rel. Wage× Rel. Wage ‑0.000 0.000 ‑0.000 ‑0.000* ‑0.000 ‑0.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) R2 0.17 0.23 0.08 0.05 0.11 0.07 Observations 995,583 765,987 995,583 923,024 923,024 726,646 Table A12: Reactions along the wage distribution Female partners Male partners Couples Employment Cond. Work hours Employment Cond. Work hours Hours gap Cond. Hours gap Rel. Potential Wage ‑0.000 0.008** 0.007 0.247*** 0.367** 0.688*** 0.002* 0.001 ‑0.006 0.062 ‑0.018 0.136 ‑0.004 ‑0.016*** ‑0.021*** ‑0.006** ‑0.018*** ‑0.028*** (0.003) (0.003) (0.006) (0.050) (0.146) (0.174) (0.001) (0.003) (0.006) (0.037) (0.077) (0.200) (0.003) (0.004) (0.004) (0.003) (0.004) (0.007) Interaction with indicator for relative wage ≥ 100% RW ≥ 100% × Rel. Wage ‑0.000 ‑0.082* 0.005*** 0.096** 0.005 0.008** (0.002) (0.046) (0.001) (0.042) (0.003) (0.003) Interaction with indicator for quantiles just around relative wage of 100% RW 90‑98% × Rel. Wage ‑0.008** ‑0.123 0.002 0.088*** 0.010** 0.010** (0.004) (0.155) (0.002) (0.028) (0.005) (0.004) RW 98.1‑102% × Rel. Wage ‑0.007* ‑0.012 0.001 0.117 0.006 0.003 (0.004) (0.124) (0.004) (0.091) (0.005) (0.006) RW 102.1‑125% × Rel. Wage ‑0.009*** ‑0.210 0.005* 0.150** 0.017*** 0.019*** (0.003) (0.125) (0.003) (0.060) (0.005) (0.005) Interaction with indicator for 5% intervals of relative wage RW 85.1‑90% × Rel. Wage 0.001 ‑0.374 0.010* ‑0.121 0.008 0.014 (0.008) (0.218) (0.005) (0.192) (0.007) (0.009) RW 90.1‑95% × Rel. Wage ‑0.019** ‑0.824** 0.011 ‑0.169 0.024*** 0.024*** (0.007) (0.332) (0.008) (0.217) (0.007) (0.007) RW 95.1‑100% × Rel. Wage ‑0.002 ‑0.367* 0.010* ‑0.028 0.014** 0.022** (0.006) (0.198) (0.005) (0.189) (0.005) (0.007) RW 100.1‑105% × Rel. Wage 0.004 ‑0.369* 0.020*** 0.127 0.011*** 0.024*** (0.006) (0.186) (0.004) (0.191) (0.003) (0.005) RW 105.1‑110% × Rel. Wage ‑0.009 ‑0.663*** 0.012* ‑0.041 0.028*** 0.036*** (0.007) (0.190) (0.006) (0.202) (0.005) (0.006) RW 110.1‑125% × Rel. Wage ‑0.008 ‑0.478** 0.013** ‑0.004 0.020*** 0.024*** (0.006) (0.185) (0.006) (0.175) (0.006) (0.007) R2 0.16 0.16 0.16 0.22 0.22 0.22 0.08 0.08 0.08 0.05 0.05 0.05 0.10 0.10 0.10 0.07 0.07 0.07 Observations 995,583 995,583 995,583 765,987 765,987 765,987 995,583 995,583 995,583 923,024 923,024 923,024 923,024 923,024 923,024 726,646 726,646 726,646 IAB‑Discussion Paper 01|2025 55 Notes: Regressions based on eq. 4 and 5. The sample includes women aged 22 and 51 with non‑missing information on the relevant variables in the years 2005‑2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. Notes: Regressions based on eq. 4 and 5. The sample includes women aged 22 to 55 and male partners aged 24‑57 years with non‑missing information on the relevant variables in the years 2005‑2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. The effects per group are measured by interacting a group dummy with the relative wage. The relative potential wages range from 75‑125%. The reference group is always the group with the lowest relative wages. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. Table A13: Employment regressions using observed couple’s wage information only Female partners Male partners Couples Employment Cond. Work hours Employment Cond. Work hours Hours gap Cond. Hours gap Relative income in couple Relative Income 0.000*** 0.000*** 0.008*** 0.014*** ‑0.000*** ‑0.000*** ‑0.006*** ‑0.011*** ‑0.001*** ‑0.002*** ‑0.001*** ‑0.002*** (0.000) (0.000) (0.000) (0.001) (0.000) (0.000) (0.001) (0.001) (0.000) (0.000) (0.000) (0.000) Rel. inc. × Rel. inc. ‑0.000*** ‑0.000*** 0.000*** 0.000*** 0.000*** 0.000*** (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) Observations 938,589 938,589 721,880 721,880 938,589 938,589 878,836 878,836 878,836 878,836 692,409 692,409 R2 0.18 0.19 0.26 0.27 0.10 0.11 0.07 0.07 0.19 0.22 0.14 0.17 Table A14: Heterogeneous effects by having child aged 0‑3 years Female partners Male partners Couples Employment Cond. Work hours Employment Cond. Work hours Hours gap Cond. Hours gap No child aged 0‑3 years Rel. Potential Wage ‑0.002 0.047*** 0.155* 0.879 0.007*** ‑0.002 0.116*** ‑0.565 0.003 ‑0.074*** 0.002 ‑0.069*** (0.002) (0.008) (0.074) (0.620) (0.002) (0.011) (0.034) (0.365) (0.003) (0.016) (0.002) (0.023) Rel. Wage × Rel. Wage ‑0.000*** ‑0.003 0.000 0.003* 0.000*** 0.000*** (0.000) (0.003) (0.000) (0.002) (0.000) (0.000) At least one child aged 0‑3 years Rel. Potential Wage 0.007 0.030 0.305** 0.881 0.005* ‑0.037 0.291*** 0.112 ‑0.013* ‑0.061 ‑0.008 ‑0.079 (0.005) (0.038) (0.116) (0.794) (0.003) (0.027) (0.038) (0.314) (0.007) (0.040) (0.008) (0.054) Rel. Wage × Rel. Wage ‑0.000 ‑0.003 0.000 0.001 0.000 0.000 (0.000) (0.004) (0.000) (0.001) (0.000) (0.000) R2 0.14 0.14 0.13 0.13 0.07 0.07 0.05 0.05 0.07 0.07 0.05 0.05 Observations 995,586 995,586 765,990 765,990 995,586 995,586 923,027 923,027 923,027 923,027 726,649 726,649 Table A15: Heterogeneous effects by having a child aged 4‑6 years Female partners Male partners Couples Employment Cond. Work hours Employment Cond. Work hours Hours gap Cond. Hours gap No child aged 4‑6 years Rel. Potential Wage ‑0.001 0.033** 0.188*** 0.988* 0.007*** ‑0.006 0.159*** ‑0.427 0.001 ‑0.068*** 0.001 ‑0.071** (0.003) (0.012) (0.064) (0.563) (0.001) (0.013) (0.033) (0.298) (0.004) (0.020) (0.003) (0.028) Rel. Wage × Rel. Wage ‑0.000*** ‑0.004 0.000 0.003* 0.000*** 0.000** (0.000) (0.002) (0.000) (0.001) (0.000) (0.000) At least one child aged 4‑6 years Rel. Potential Wage ‑0.000 0.080** ‑0.002 0.506 0.005 ‑0.029 0.087 ‑0.138 ‑0.001 ‑0.093 0.002 ‑0.084 (0.006) (0.029) (0.082) (0.433) (0.003) (0.021) (0.056) (0.841) (0.009) (0.057) (0.010) (0.074) Rel. Wage × Rel. Wage ‑0.000** ‑0.002 0.000* 0.001 0.000 0.000 (0.000) (0.002) (0.000) (0.004) (0.000) (0.000) R2 0.09 0.09 0.13 0.13 0.07 0.07 0.05 0.05 0.05 0.05 0.04 0.05 Observations 995,586 995,586 765,990 765,990 995,586 995,586 923,027 923,027 923,027 923,027 726,649 726,649 IAB‑Discussion Paper 01|2025 56 Notes: Regressions based on eq. 4 and 5. The sample includes women aged 22 and 51 with non‑missing information on the relevant variables in the years 2005‑2019. The relative income is measured as the ratio between the female and the male net monthly income in a couple. Also zero incomes are included. Standard errors clustered by state. * p < 0.10, ** p < 0.05, *** p < 0.01. Source: Own calculations based on Microcensus 2005‑2019. Notes: Regressions based on eq. 4 and 5. The sample includes women aged 22 to 55 and male partners aged 24‑57 years with non‑missing information on the relevant variables in the years 2005‑2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. The effects per group are measured by interacting a group dummy with the relative wage. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. Notes: Regressions based on eq. 4 and 5. The sample includes women aged 22 to 55 and male partners aged 24‑57 years with non‑missing information on the relevant variables in the years 2005‑2019. Standard errors clustered by state in parentheses. * p < 0.10, ** p < 0.05, *** p < 0.01. The effects per group are measured by interacting a group dummy with the relative wage. Source: Own calculations based on Microcensus 1995/96 & 2005–2019, SIAB 2005–2019 and BIBB 1998/99. IAB‑Discussion Paper 01|2025 63 ........... ............................................. ........................... ............................................... ............................................ .............................. ........................... 57 58 59 60 61 Table A16: Heterogeneous effects by motherhood of child aged 7‑18 years Table A17: Heterogeneous effects by motherhood of child ............................... 57 Table A18: Educational level of female partner Table A20: Heterogeneous effects by type of education‑match Table A22: Effects of relative wage for singles Table A24: Characteristics by partnership status Table A19: Educational level of male partner ............................................... 58 Table A21: Heterogeneous effects by type of age difference 59 Table A23: Likelihood to be living in a cohabiting partnership 60 Imprint IAB-Discussion Paper 01|2025 Publication Date January 27, 2025 Publisher Institute for Employment Research of the Federal Employment Agency Regensburger Straße 104 90478 Nürnberg Germany All rights reserved This publication is published under the following Creative Commons licence: Attribution -- ShareAlike 4.0 International (CC BY-SA 4.0) https://creativecommons.org/licenses/by-sa/4.0/deed.de Download https://doku.iab.de/discussionpapers/2025/dp0125.pdf All publications in the series ``IAB-Discusssion Paper'' can be downloaded from https://iab.de/en/publications/iab-publications/iab-discussion-paper-en/ Website https://www.iab.de/en ISSN 2195-2663 DOI 10.48720/IAB.DP.2501 Corresponding author Luisa Hammer 0911 1773004l E-Mail [email protected]