**The RRS data show that when couples have children, husbands deliver more labor supply and,**

**conditional on labor status, husbands and wives increase the home production time.** The fifth functional form assumption is that children affect the flow utility directly through changes in household type-specific tastes for spouses’ leisure �α � and for household production (α3). To identify those six parameters, we use changes in time allocation, comparing couples with and without children as well as CC CC AA change information in all the steady states (see figure 3 and table A2 in the appendix).

**Flabbi and Mabli** ( **2018) established that for unitary models with leisure and consumption, the flow utility’s risk aversion parameters are identified from the interdependence of spouses` decisions in the labor market.** The model introduces time in household production as another identification source for couples’ simultaneous choices. Figure 3 shows that males’ home production time allocation can range from almost 27 percent when NP or UE to 6 percent when males have a FT job. The observed degree of reduction of home production and leisure that spouses exhibit across different labor market states provides the identification for the risk-aversion parameters. The intuition is as follows: if the household is risk averse for male leisure, then the parameter will tend to zero. Thus, males will demand almost the same leisure in any labor market state. On the contrary, if the risk aversion parameter tends to 1, males will reduce the consumption of leisure significantly when changing the labor market state. The same will apply to home production, but as home production is a public good for the household, identification is trickier.

**Defining the household production function is vital for the model to capture the trade-off between working and home production, and the substitution/complementarity that wives’ and husbands’ times exhibit in the data** . If the production function is linear, spouses’ times in home production would have large substitution: that is, if a wife gives more time to chores, the husband can spend significantly less time in home production. If the production function is Cobb-Douglas, then home production time could not be close to zero by a spouse. In the literature, Gayle and Shepard (2016) used a Cobb-Douglas function that employed spouse time as inputs. Albanesi and Olivetti (2009) and Siegel (2013) used a constant elasticity of substitution (CES). Choi (2018) used a Cobb-Douglas composed by a CES: the CES part was explaining the chores time that spouses were performing, while the Cobb-Douglas was between the CES output and the economic resources that any additional children demand.

**The sixth functional form assumed is a CES for the home production function.** It was chosen because the CES can characterize a Cobb-Douglas or a linear function. This flexibility should help the model to fit the data better, and the θ parameter is identified through spouses’ times in household

> 24 Consumption by household is equal to household income: i h h i . No information about expenditures is available in the database. Including the costs of inputs for a household and the cost of raising children could be areas of future ii ii ii ii cc = ww + ww + yy research. Including these features would raise the model’s heterogeneity and/or the decision space.

> 25 The vectors are defined as follows: β′ = {δ, β1, β2, β3}; α′ = {α , α , α3 }. 17 CCMM CCWW CC