**husbands’ labor participation, but does not change wives’ labor participation time.** Roma households without children will allocate more time to husbands, as their leisure is the individual factor that weights the most in the flow utility. However, when children are present, as husbands’ leisure weight parameter decreases, husbands will reduce leisure at any labor market state. Simultaneously, spouses will allocate more time to home production, as it weighs more in the flow utility. Female leisure is weighted almost the same, and, by complement, consumption now weighs more in the flow household utility. These are the elements that help explain why husbands increasingly enter the labor market and wives allocate more time to home production when having children.

|Parameter<br><br>|**Table 3: Estimated parameters, meaning, and arrival**<br>Description|**time**<br>Male<br>Female|
|---|---|---|
|λA|job offers to unemployed|0.09<br>0.08|
|ηA<br>PT<br><br>|termination shock to part-time employed|0.04<br>0.04|
|ηA<br>FT<br><br><br><br><br>|termination shock to full-time employed|0.04<br>0.04|
|μwage_A<br>PT<br><br><br>|lognormal part-time wage offer location parameter|2.48<br>2.40|
|μwage_A<br>FT|lognormal full-time wage offer location parameter|1.78<br>1.60|
|σwage_A<br>PT<br><br><br>|lognormal part-time wage offer scale parameter|0.46<br>0.41|
|σwage_A<br>FT<br><br><br>|lognormal full-time wage offer scale parameter|0.52<br>0.52|
|p<br><br><br><br><br>|probability of part-time job offer|0.31<br>0.31|
|αA<br>c<br><br><br>|weight of leisure when having children|0.278<br>0.271|
|α3<br>c<br><br><br>|weight of home production when having children|0.15|
|αA<br>lc<br>|weight of leisure when no children|0.283<br>0.271|
|α3<br>lc<br>|weight of home production when no children|0.14|
|δ<br><br><br><br>|CRRA consumption parameter|0.10|
|βA<br>|CRRA leisures parameters|0.39<br>0.63|
|β3<br><br>|CRAA home production parameter|0.11|
|μA_γ<br><br>|exponential home production parameter|1.00<br>1.85|
|γH<br><br>|home productivity of the high type|3.32|
|θ<br><br><br><br>|home production CES substitution parameter|0.20|
|τC<br>|arrival rate of children|0.01|
|τNC|children leave the house|0.005|
|sA<br><br>|search cost<br>_Source:_Authors’ calculations.|0.82<br>0.74|

**Table 3 also shows that high household productivity types are 3.3 more productive than low productivity types. The CES parameter, θ, is equal to 0.20** ; this means that Roma spouses’ home production times presents higher substitution than in a Cobb-Douglas (θ=0), but they are still far from being a linear production function (θ=1).

**Arrival rates of the labor market show that husbands have an advantage in the labor market. They receive job offers more often; and once they accept one, the laid-off shock will occur less frequently.** The model’s unit of time is a month, so for example λ means that unemployed males receive 0.09 job offers in a month. The model predicts that about 30 percent of the overall job offers for MM males and females are part-time offers.

**Table 4 shows the relevant implied values for the estimated wage offer distributions and the implied durations (in months) consistent with Poisson arrival shocks.** We found that unemployed males receive job offers slightly more frequent than unemployed women (11.3 vs. 11.9 months,

20