Parental time and working schedules

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.

Appendix

1.1 Appendix 1: list of control variables in the two-regime 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 5-year groups); number and age of children (polytomous—15 groups); for non-working fathers, for single mothers and in the three-regime models, we used only two continuous variables: the age of the youngest child and the number of less than 18-year-old 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 5-year groups); age of the youngest child and square age (continuous); number of less than 18-year-old 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).

1.2 Appendix 2: a switching regression model with three regimes and endogenous switch

Let us consider the following model:

$$ \begin{array}{*{20}l} {{y_{{0i}} = X_{{0i}} \beta _{0} + u_{{0i}} } \hfill} \\ {{y_{{1i}} = X_{{1i}} \beta _{1} + u_{{1i}} } \hfill} \\ {{y_{{2i}} = X_{{2i}} \beta _{2} + u_{{2i}} } \hfill} \\ {{I^{*}_{{0i}} = 0} \hfill} \\ {{I^{*}_{{1i}} = Z_{i} \gamma _{1} + \varepsilon _{{1i}} } \hfill} \\ {{I^{*}_{{2i}} = Z_{i} \gamma _{2} + \varepsilon _{{2i}} } \hfill} \\ \end{array} $$

(6)

$$ I_{i} = m{\text{ if }}I^{*}_{{mi}} = {\mathop {\max }\limits_{k = 0,1,2} }{\left( {I^{*}_{{ki}} } \right)} $$

(7)

$$ y_{i} = y_{{mi}} {\text{ if }}I_{i} = m $$

(8)

$$\begin{array}{*{20}l} {{{\left( {u_{0} ,u_{1} ,u_{2} ,\varepsilon _{1} ,\varepsilon _{2} } \right)}\prime \sim N{\left( {0,\Sigma } \right)}\quad \Sigma = {\left( {\begin{array}{*{20}c} {{\Sigma _{u} }} & {{\Sigma _{{u,\varepsilon }} }} \\ {{{\sum\nolimits_{u,\varepsilon }^{} \prime }}} & {{\Sigma _{\varepsilon } }} \\ \end{array} } \right)}} \hfill} \\ {{\Sigma _{u} = {\left( {\begin{array}{*{20}c} {{\sigma _{0} }} & {{\sigma _{{01}} }} & {{\sigma _{{02}} }} \\ {{\sigma _{{01}} }} & {{\sigma _{1} }} & {{\sigma _{{12}} }} \\ {{\sigma _{{02}} }} & {{\sigma _{{12}} }} & {{\sigma _{2} }} \\ \end{array} } \right)},\Sigma _{\varepsilon } = {\left( {\begin{array}{*{20}c} {1} & {{\sigma _{\varepsilon } }} \\ {{\sigma _{\varepsilon } }} & {1} \\ \end{array} } \right)},\Sigma _{{u,\varepsilon }} = {\left( {\begin{array}{*{20}c} {{\begin{array}{*{20}c} {{\sigma _{{0,\varepsilon _{1} }} }} & {{\sigma _{{0,\varepsilon _{2} }} }} \\ \end{array} }} \\ {{\begin{array}{*{20}c} {{\sigma _{{1,\varepsilon _{1} }} }} & {{\sigma _{{1,\varepsilon _{2} }} }} \\ \end{array} }} \\ {{\begin{array}{*{20}c} {{\sigma _{{2,\varepsilon _{1} }} }} & {{\sigma _{{2,\varepsilon _{2} }} }} \\ \end{array} }} \\ \end{array} } \right)}} \hfill} \\ \end{array} $$

(9)

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:

$$ L = {\sum\limits_{m = 0,1,2} {f{\left( {Y = y_{m} \left| {I = m} \right.} \right)}P{\left( {I = m} \right)}} } = {\sum\limits_{m = 0,1,2} {f{\left( {Y = y_{m} } \right)}P{\left( {I = m\left| {Y = y_{m} } \right.} \right)}} } $$

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.