The domestic chores on which we focus are house cleaning, dishwashing, laundry and ironing. These are routine tasks performed in virtually every household. Furthermore, these are tasks that few people report enjoying. This is important as individual enjoyment of housework activities (process benefits) may obscure estimates of the price effects. Couple households in the USA spend about 10.5 hours per week on these tasks. Our data indicate that couples in the UK spend an average of almost 12 hours, while those in France spend just over 14 hours per week on domestic services thus defined. This constitutes a substantial time commitment, equivalent to over 1.5 days of full‐time employment. As these activities constitute an undesirable time burden, it is reasonable to suppose that households would seek alternative inputs to reduce that burden. The alternative inputs include maids, who typically provide just these services, and time‐saving household appliances, like dishwashers.a
Our econometric model consists of a system of six equations estimated jointly by simulated maximum likelihood. One equation models households hiring a maid, another equation models households having a dishwasher, and four equations model the time spent by each partner on housework on weekday and weekend days. In both the UK and France, we find that higher maid prices are associated with more weekend but not weekday time, suggesting that maids services is a closer substitute for weekend than weekday time, and hence that labour supply effects might be small. In addition, for both countries, we conclude that women’s opportunity cost of time has a significant impact on all decisions, while men’s is important mainly in determining the use of appliances and maid service. Thus the higher her opportunity cost of time, the more time he spends and the less time she spends on housework, while the higher each partner’s opportunity cost, the more likely the household is to have maid service and a dishwasher.

1 Empirical Specification
Our empirical approach is to model jointly the various inputs to domestic production for each household. Following Aguiar and Hurst (2005) and Hamermesh (2007), we employ linear specifications to model the housework time inputs as a function of prices. Following Lundberg (1988), we simultaneously model these time inputs. Both the decision to hire a maid and the availability of appliances are estimated using probit specifications.

Let hijk represent the time (in minutes) spent on domestic work by household member k (k = m, f) of household i (i = 1, …, N) on day j (weekend, weekday). Let wim and wif represent the opportunity costs of time for the husband and wife, respectively.a The price of domestic services purchased from the market is pd, and the price of appliances is pa. We also allow demand to be affected by other household (e.g. non‐labour income and household composition) and individual (e.g. age and education) characteristics z and an error term u. The four equations for own housework time have the form:

urn:x-wiley:00130427:media:ecca12083:ecca12083-math-0001(1–4)
The probability of hiring a maid (di) and the probability of having time‐saving appliances (ai), here a dishwasher, are modelled with a probit specification using the same covariates:

urn:x-wiley:00130427:media:ecca12083:ecca12083-math-0002(5)
urn:x-wiley:00130427:media:ecca12083:ecca12083-math-0003(6)
We estimate equations (1) to (6) by simulated maximum likelihood using the Geweke, Hajivassiliou and Keane (GHK) algorithm (for an application in Stata, see Roodman 2007, 2009). As all the price measures are in log form, the coefficient estimates to the price measures in the linear specifications are interpretable as the impact of a doubling of price on time. In the case of the purchased time and appliance probit specifications, we report both coefficient estimates and marginal effects.

By estimating these six equations jointly, our specification allows us to estimate the degree to which unobservable factors affecting the demand for different time inputs in the household production of domestic services are correlated. Estimating these cross‐equation correlation terms will improve the efficiency of our parameter estimates, but may also shed light on other factors affecting input demand. As each partner provided information on both a weekday and a weekend day in the UK, residuals are available for all six equations for every household, so a full set of correlation terms (15) can be estimated for the UK sample. For France, because time diaries were collected on only one day, we are able to estimate only four equations/four residuals for every household. This means that we can estimate only eleven correlation terms for the French data. We are unable to observe how his (her) time is correlated (in the residuals) between weekend and weekday days or to measure how his time on one type of day is correlated with her time on the other type of day.

In general, we expect that the greater a single input price, all else constant, the less of that input will be used in production because that input has become relatively more expensive. Cross‐price effects are likely positive as these inputs are substitutes for one another in home production, but the magnitude and possibly even the direction of these effects will depend on the degree to which hf, hm, d and a are substitutes and the relative productivity of each resource. In addition, the scope for substitution of partners’ time inputs and market inputs may vary over different days of the week as a result of variation in either individual time budgets or household needs. Individuals employed on weekdays tend to have more time available to perform housework on the weekend. On the other hand, some domestic tasks—like doing the dishes—may need to be performed every day, while others—like laundry and ironing—may be more readily deferred. Given the fixed costs associated with maids services, it is unlikely that a maid would come every day to perform services, hence we hypothesize and examine empirically whether maids services is a better substitute for tasks that can be deferred and completed on the weekend.