it appears to be the case that unobservant that affect the probability of having maids services or a dishwasher are also likely to reduce time spent on housework. Of these 16 correlation terms, 13 are negative—all eight relating to weekday time and five of those significantly so. This negative correlation is particularly strong between maids and women, and between dishwashers and men. We observed earlier that her value of time had a somewhat greater marginal impact on the probability of having maids services, while his value of time had a greater marginal impact on the probability of having a dishwasher, so this relation is not simply an expression of opportunity costs but may reflect individual preferences regarding the tasks involved. While we have restricted our analysis to tasks that individuals do not generally enjoy, preferences may still vary. Those who enjoy these activities the least are likely to spend less time on housework and be more likely to purchase the services.
Also estimable in both countries are the correlations between partners and within day type. Here we find that the correlations between the unobservables affecting his and her domestic work are positive on weekend days and negative on weekdays. This relation is statistically significant in France on both weekdays and weekend days, and in the UK on weekdays. Weekend schedules are less likely impacted by employment schedules, and the positive relation on weekend days may reflect common preferences for home‐produced goods or possibly shared production time. There is often less flexibility on weekday schedules, and housework performed on these days may ‘need’ to be performed on these days. The negative relation in the unobservables on weekdays may indicate that what one partner does on a weekday spares the other partner from the task. Thus there appears to be more substitution between partners on weekdays than on weekend days.
As discussed earlier, it is possible to estimate the cross‐day correlation terms only in the UK. These estimates indicate that individuals who spend more time on housework on weekend days for unobservable reasons are also likely to spend more time on housework on weekdays for unobservable reasons. These positive correlations could be the result of a number of different mechanisms. For example, they could reflect individual preferences over home production or productivity in home production. Between partners, between days correlations are consistently negative and statistically significant. Thus when he (she) reports more time on a weekend day for unobservable reasons, she (he) reports less time on a weekday day.
Several alternative specifications were estimated to examine the robustness of these results. In deference to Stewart’s (2013) concerns about the meaning of zero time values in diary records of time use, all the household time‐use equations discussed above were estimated using ordinary least squares (OLS). Stewart (2013) was perhaps the first to argue that individuals reporting no time spent on housework on a given day may actually do some housework the next day—implying that zeros in housework deserve different treatment than zeros in labour supply. The zeros in housework are random and capture infrequency rather than censoring. In this case, Tobit need not (and should not) be used. More than 60% of French men and 50% of British men report spending no time on housework on a given day. Runs using a Tobit specification for all of the men’s housework time equations yielded wage estimates of the same sign and level of significance as reported in the OLS specifications.
We also estimated the basic model restricting our sample to dual earner couples as in Friedberg and Webb (2007). To this end, we generated new imputed wage measures that did not include controls for sample selection, that is, were conditional on employment. The results for the price effects in the UK were very similar, with two exceptions. First, the marginal impact of her predicted wage on his weekend time, while still of the same magnitude, is now significant at only the 15% level. Second, the impact of her predicted wage on her weekday time, while still negative, becomes statistically insignificant. The price effects in both the maid and the dishwasher equations remain highly statistically significant. In France, her opportunity cost of time continues to have the same associations with household time use in each equation, but with substantially reduced statistical significance. Only in her weekday time equation does her predicted wage remain significant at the 1% level. Again, both his and her opportunity costs of time remain highly significant in both the maids services and dishwasher equations. In both countries, we continue to find a stronger relation between her opportunity cost and hiring a maid, and between his opportunity cost and having a dishwasher. The price of maid service also appears to have a somewhat larger effect in most equations.
As cohabiting couples displayed somewhat different behaviour in the basic model, we tested two alternative specifications. Restricting the analysis to married couples alone yielded results not noticeably different from those for the full sample. Using the full sample but distinguishing between the earnings of married and cohabiting partners yielded no significant differences in the case of the French data, where all cohabiting women tend to spend less time on housework, while there were some differential effects by ‘his’ wages in the UK. Specifically, women cohabiting with men in the UK who have a higher opportunity cost of time appear to spend significantly less time on housework on weekdays and somewhat less time on housework on weekend days. One possible explanation for this result is that cohabiting women in the UK are able to exert more power than married women only if their partner has higher earnings potential.
Finally, in recognition that we have severely restricted our definition of housework to focus on activities that are typically viewed as women’s tasks (cleaning, laundry, ironing and dishwashing), that there are other housework tasks that are primarily performed by men (for evidence regarding gardening in France, see Stancanelli and van Soest 2012), and that households may specialize by gender and trade off these tasks, we re‐estimate the model including time spent on yard work and gardening in our measures of time use. This increases the time reported by women in the UK by approximately 10%, while increasing the time reported by men in the UK by 50–90%. More time still is spent on these activities in France. Women’s reported time increases by 10% on weekdays and 25% on weekend days, while men’s increases fourfold to fivefold (albeit from very low levels). The UK estimates change very little. The most notable change is that the price of maid service becomes statistically insignificant in his weekend time‐use equation—a result that one might expect since maids do not generally perform yard work. In the case of France, his opportunity cost loses statistical significance as a determinant of her weekday time, and hers loses any significant relation to his time use, while his opportunity cost becomes significantly negatively related to his weekday time. These French results might be interpreted to mean that her opportunity cost has a greater impact on his time spent on ‘her’ tasks (cleaning), while his opportunity cost has a greater impact on his time spent on ‘his’ tasks (gardening). However, it should also be noted that many French men and women report enjoying gardening, and the substantial amount of time reported in this activity may be indicative of process benefits and reduce any association with opportunity costs.
Sensitivity tests were also conducted with respect to the specification of opportunity costs. We experimented with different measures for the price of maid service (see notes 15 and 16) as we believe that the weak significance of this variable is largely attributable to its poor measurement, but these alternative measures did not improve the fit. We estimated the model with alternative measures of predicted wage, with substantially the same results. We also used propensity score matching to generate opportunity costs as an alternative to predicted wages. The matched wages have a much higher standard error than the predicted wages, and correspondingly tend to have a smaller marginal impact. In each country, the opportunity cost effects on maid services and dishwashers were of a similar sign and at least as statistically significant. The same is true of the impact of opportunity costs in the household time equations in each country, though the results lose statistical significance in all but the women’s weekday time equations in France. In general, our demand system results are quite robust to changes in the sample and to alternative measures of input price.