Abstract
This paper investigates the effects of working schedules and of other characteristics (including family composition) on the time devoted by mothers and fathers to different activities with children in Canadian households, by using 1992 and 1998 Canadian Time Use Surveys. Switching regression models and models with selection allow us to simultaneously model labour market participation, type of work schedules and allocation of parental time. Working time has a negative and very significant effect on parental time. Hours worked during the day or at night exert a similar effect on parental time, but the impact of hours worked in the evening is by far larger. Time worked in the evening mainly decreases leisure and social activities with children.
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Notes
According to Nock and Kingston (1988), they spend more time watching TV with their children.
This differs, for example, from the Swedish household panel study (Household Market and Non Market Activities; see, Hallberg and Klevmarken 2002) in which no fixed format was used for activities (the respondent’s own words were recorded). See also, for example, Juster and Stafford (1991) for a discussion about the advantages and shortcomings of the different types of time use surveys.
A few categories are excluded from our analysis: category 12 (sleep), as respondents were not asked with whom they were while sleeping; category 24 that concerns residual codes (missing information); categories 1–3 and category 11 that refer to paid work and school activities of respondents and which are rarely conducted in the presence of children.
This could be verified with the 1998 General Social Surveys data.
However, respondents were asked to evaluate the total amount of time spent in childcare by the other parent during the week preceding the survey, but this measure is rather imprecise.
Note that biological and stepchildren are not distinguished in the public data files. Moreover, in 1992, variables describing family composition do not allow us to distinguish children aged between 13 and 18, whereas in 1998, children between 13 and 14 and between 15 and 18 can be differentiated.
The two surveys were pooled to increase the sample size.
That is 3.1% on 18.0%
Increase of 7.4 from 37.0%
Presser (2004) argued that the data used by Beers do not allow him to draw such a conclusion because of comparability problems; there are no such comparability problems with our data.
Compared to the means, standard deviations are much larger for the average parental time of respondents whose working hours on the Designated Day cut through more than one period. This indicates that these situations are probably more diverse than others.
As usual, RHS is for Right Hand Side.
It is more simple to compute but less efficient than the Amemiya Generalized Least Square Estimator.
The Smith and Blundell test, which allows to test endogeneity in tobit models, is not exactly adapted to our problem because it assumes that the potentially endogenous variables are continuous, whereas our variables are limited. However, under the assumption of continuity, we may consider that work schedules are not endogenous.
Hallberg and Klevmarken (2002) found that total individuals’ own and their spouse’s market hours can generally be considered as exogenous variables when estimating parental time. This gives some indications on how total working time and parental time are chosen, even if this cannot provide any information on the effects of schedules.
We thank an anonymous referee for having pointed this problem.
As it is wellknown that the secondstep matrix of variances–covariances is biased, it is corrected by applying the Murphy and Topel’s (1985) method. In particular, this requires the computation of the derivatives of the Mills ratios with respect to the different parameters. Analytically, those derivatives are easy to compute; however, the derivative with respect to ρ, the correlation between the two firststep residuals, cannot be easily computed, as it involves the derivative of the bivariate normal cumulative distribution function with respect to ρ, which is numerically difficult to evaluate. For this reason, for each point of the sample, the derivatives functions of the Mills ratios with respect to ρ have been numerically approximated and then evaluated at the estimated value of ρ.
For example, for mothers, there is a very strongly positive effect associated with having worked at 3 a.m., compared to the strong negative effect of having worked at 2 a.m. However, there is only one mother who has worked at 3 a.m. and not at 2 a.m., so that identification is based on a single observation. The effect of having worked at 2 a.m. or at 3 a.m. is probably of a similar magnitude as that of having worked at 1 a.m. or at 4 a.m. (that is approximately the average of the effect of having worked at 2 a.m. or at 3 a.m.).
Partners’ work schedules have been reported by the respondent and are thus less precisely measured than own work schedules; for this reason, we used only dummy variables.
The size of the working single mothers sample is nevertheless quite small (especially for subsample of mothers who work nonstandard schedules).
In the alternative specification, we have also introduced a variable indicating whether the respondent has worked a split shift (more than 3 h between two spells of work) during the Designated Day. Both mothers and fathers who had worked a split shift have increased direct childcare.
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Acknowledgements
We thank participants to the conference, especially Daniel Hallberg, for their helpful comments. We also thank David Margolis for helpful discussions on econometrics. We also thank the two anonymous referees whose comments greatly helped to improve our paper. All remaining errors are ours. Support for this study was provided by grants from the Social Science and Humanities Research Council of Canada (regular grant and strategic grant on Social Cohesion). The analysis is based on data collected by Statistics Canada, but does not represent the views of Statistics Canada. The detailed results of all the complete models estimated in the paper are available upon request from the authors.
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Appendix
Appendix
Appendix 1: list of control variables in the tworegime model

1.
Predicting parental time
Only for working respondents: respondent’s number of hours worked the Designated Day during the day, during the night and in the evening (continuous); respondent sometimes works at home (dichotomous); respondent has flexible schedules (dichotomous); respondent usually works rotating shift (dichotomous); respondent’s professional occupation (polytomous).
For all respondents: partner’s work schedules (dichotomous variables indicating whether the respondent has worked during the day, in the evening or during the night the Designated Day); time spent by the partner with children in the previous week (continuous); time spent by the partner with children is missing (dichotomous); respondent interviewed on Saturday or Sunday (dichotomous); age of respondents (continuous, by 5year groups); number and age of children (polytomous—15 groups); for nonworking fathers, for single mothers and in the threeregime models, we used only two continuous variables: the age of the youngest child and the number of less than 18yearold children; respondent’s educational level (polytomous); respondent born in Canada (dichotomous); respondent’s region of residence (polytomous); respondent sometimes goes to church (dichotomous).

2.
Probability of participating to the labour market (switch part of the regression)
1998 survey (dichotomous); respondent’s age and square age (continuous by 5year groups); age of the youngest child and square age (continuous); number of less than 18yearold children (continuous); respondent’s educational level (polytomous); respondent born in Canada (dichotomous); respondent’s mother born in Canada (dichotomous); respondent’s father born in Canada (dichotomous); home owner (dichotomous); respondent’s region of residence (polytomous); dummy variable indicating whether the partner of the respondent participates in the labour market (except for single mothers).
Appendix 2: a switching regression model with three regimes and endogenous switch
Let us consider the following model:
y is the dependent variable. I _{ i } indicates to which regime individual i belongs (0, 1 or 2).
As we only observe I _{ i } and not \(I^{*}_{i} ,\) we normalise the variances of the ɛ’s to 1. Moreover, people are never observed in several regimes. As a consequence, the \( \sigma _{{ij}} \;{\left( {i = 0,1,2;i \ne j} \right)} \) will not appear in the likelihood and cannot therefore be identified.
The likelihood of an observation can be written:
where \( f{\left( {Y = y_{m} } \right)} = \varphi {\left( {y_{m} ;0,\sigma _{m} } \right)} \) is the density of Y in the regime m.
The computation of the marginal probabilities only requires the cumulative of the binormal distribution.
This model can easily be extended for M regimes, with M ≥ 2. However, it involves the computation of the cumulative of the (M − 1) normal distribution and thus requires, for M > 3, the use of a Geweke–Hajivassiliou–Keane simulator, for example.
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Rapoport, B., Le Bourdais, C. Parental time and working schedules. J Popul Econ 21, 903–932 (2008). https://doi.org/10.1007/s0014800701476
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DOI: https://doi.org/10.1007/s0014800701476
Keywords
 Parental time
 Switching regression models
 Working schedules
JEL Classification
 C3
 J13
 J22