**For equation 2, represents the current children possession, while represents the opposite state, once a fertility shock is in effect.** The second term on equation 2 represents the event where CC ¬CC the husband receives a job offer, the available wages offered are represented with , and the PT or FT schedules are represented with h<sup>′</sup> . When the household faces a new job offer, the spouses can choose ww<sup>′</sup> between four labor choices, the first of which is that both spouses work at the current wages. If a new offer is accepted by the husband then the three remaining choices are possible: the wife keeps her current job, the wife moves to unemployment, or the wife moves to nonparticipation. Also, for each labor state, the couple needs to decide how much chore time each spouse will perform. If a fertility shock arrives, then the valuation of the available choices changes, in which case the couple will move to a new maximizing state in terms of the labor market and chore time decisions.

**Given that the household moves to the maximum states from the options made available by the shock, with known value functions, simple decision rules were applied to represent households’ behavior.** Then, with a closed-form solution for the value functions, for every state, we could identify the acceptable minimum wage (reservation wage) for which a spouse would accept a job offer, and for what amount the working spouse would endogenously quit (if he/she had a job). Given the complexity of household interactions and the endogeneity that both spouses’ decisions have, the alternative chosen in this paper applies fixed-point algorithms over the value functions until numerical convergence is achieved for the states on every wage and time allocation that a household might select.

**This environment increases the model’s outputs and the possibility of discussing gender gaps in time use, and also allows us to develop a framework that explains in more detail the observed labor market gender gaps.** Conditional that each spouse belongs to a particular home productivity type, our mechanism works as follows: husbands and wives of the high home productivity type will allocate more time to home production, relative to their low home productivity counterparts. This characteristic will be active at any labor market state that the couple might be in: for high productivity types, the labor market options are less appealing since eventually they will need to give up home production time. Gender search costs will be shared by all husbands and wives and will directly affect the nonparticipation or unemployment decision. Therefore, high home productivity husbands and wives have a higher probability of staying out of the labor market because the value of their nonmarket option is high. Conversely, low home productive types will participate more in the labor market and given that production at home is not so valuable, they are more prone to work; consequently, they are more willing to accept jobs at lower wages.

**Thus, the heterogeneity in our model has both impacts on the allocation between leisure and home production, and a direct effect on participation rates and accepted wages.** The framework in this paper, including spouses as the unit of study,<sup>11</sup> helps to disentangle whether observed gender gaps are due to differences in the labor market or differences in gender roles regarding leisure and home production.

# **3. Stylized Facts for the Regional Roma Survey Sample**

**This paper relies on data from the 2017 Regional Roma Surveys (RRS), the most comprehensive surveys to date on income, living conditions, and human development outcomes among**

> 11 Modeling other adults’ decisions is out of the scope of this paper because including them as decision-makers will increase the household decision space substantially.

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