Abstract
In this study we examine the collective labor supply choices of dual-earner parents and take into account child care expenditures. For this purpose we use data of the Flemish Families and Care Survey (FFCS, 2004–2005). The main findings are, firstly, that the supply of paid labor is hardly affected by changes in the prices of child care services. Secondly, child care price effects on the individual labor supplies are much smaller than the wage effects. Thirdly, we find that additional earnings due to an increase in household non-labor income minus the child care expenditures are mainly transferred to the wife.
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Notes
The utility function of parent s under caring preferences can be represented as: U s = f s(u m(X m, Q, l m), u f(X f, Q, l f)), s = m, f (see Becker 1991).
The proof is given in Chiappori (1992).
In addition it holds that the sharing rule is identifiable up to an additive constant κ(z) when we would assume that preferences and the sharing rule are simultaneously influenced by certain preference factors (z).
Labor supply would depend on the spouse’s wage when we would assume caring preferences and the demand function of parent m would then write: \(h^{m}=\Lambda^{m}(w_{m},w_{f},\rho(w_{m},w_{f},\tilde{y},d,z),z)\).
Theoretically, this restrictions means that it cannot be the case that \(\frac{\partial h^{m}/\partial\tilde{y}}{\partial h^{f}/\partial\tilde{y}}\) equals \(\frac{\partial h^{m}/\partial d}{\partial h^{f}/\partial d}\).
See Chiappori et al. (2002). Furthermore, we have that \(\frac{\partial}{\partial w_{f}}\left(\frac{BC}{D-C}\right)=\frac{\partial}{\partial w_{m}}\left(\frac{AD}{D-C}\right)\) which is similar to \(\frac{\partial}{\partial w_{f}}\left(BC\right)=\frac{\partial}{\partial w_{m}}\left(AD\right)\). When we substitute A, B, C, D and determine these derivatives we have that \(\frac{\alpha_{6}\beta_{5}}{\alpha_{4}\beta_{4}w_{m}w_{f}} = \frac{\beta_{6}\alpha_{5}}{\alpha_{4}\beta_{4}w_{m}w_{f}}\) which simplifies to α 6 β 5 = β 6 α 5.
Net hourly wages refer to wages net of taxes and social security contributions as reported by the respondents (“take away pay”). Wages are expressed in hourly amounts through a division of the stated monthly labor income by the reported “usual weekly working hours” (multiplied by 4.33). To avoid division bias we used the latter, rather than the observed weekly working hours in the reference week that we use as an indicator of working hours (see text).
Bivariate Anova tests gives F-values that do not reach any of the conventional thresholds for statistical significance (women, F-value 0.03 and men 0.25 with 1 and 381 degrees of freedom).
Moreover, self-employed workers are more likely to have irregular working hours (statistically significant bivariate Anova test results not shown). This particular characteristic is reflected separately in the empirical specification (see below).
This is a basic trait of the collective approach to household modeling. The Pareto optimal character of the outcome is assumed, without specifying a particular solution concept.
Children are allowed to start pre-primary school on the first of five entry moments (after holiday periods) after they have reached the age of 30 months. Hence, many children enter pre-primary school slightly before their third birthday.
In some economic sectors, collective agreements allow for longer career breaks (up to five years). Furthermore, it is interesting to know that the benefit given during career breaks is considerably lower than the benefit for parental leave.
Another issue is the endogeneity of wages. We have instrumented the individual (log) wages using third order polynomials for age, a set of education dummies, a set of living region dummies, a dummy variable that indicates whether a person is an entrepreneur and family size. Because the data did not provide us with a good instrument, the exogenous wage variation that is predicted is entirely driven by the functional form that is chosen. Moreover, the SUR estimation results yielded rather similar results and, therefore, we use the observed wage rates instead of the instrumented wage rates in this paper.
If we would separately estimate the first and second stage model this would yield incorrect residuals, because they are computed from the instruments rather than the original variables (Wooldridge 2009). All statistics computed from those residuals would therefore be incorrect as well (i.e. variances, estimated standard errors, etc.). By using the STATA ivreg2 routine described in Baum et al. (2007) we obtain standard errors robust to the violation mentioned above.
For the sake of robustness, we also tested if α 4 · β 6 = α 6 · β 4 and if α 5 · β 6 = α 6 · β 5 and found similar results (i.e. \(\chi_{0.01}^{2}=10.11\) for (1) and \(\chi_{0.01}^{2}=0.54\) for (2)).
We do not include child variables as preference factors, such as the number of pre-school children and family size, as they are correlated with the child care benefits and the child care demand included in \(\widetilde{y}_{n}\). We note that these child variables are insignificant when we include them in the labor supply functions, and this is likely caused by the \(\widetilde{y}\) variable that captures this effect.
For these predictions we used the price of formal child care which is on average 2.77 euro for the households in our sample.
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Acknowledgements
We are grateful to Pierre-André Chiappori, the editor and one anonymous referee for their helpful comments.
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Appendix
Appendix
In this appendix, we show that productive efficiency requires the individual child care supply functions to depend on wages, just like labor supply. Let us consider the Lagrangian maximand \(\mathcal{L}\) using the maximization program in Eq. 5, i.e. \(\max_{h^{s},c^{s}}U^{s}(u^{s}(X^{s},1-c^{s}-h^{s}),H,Q)\). By assuming interior solutions, we can disregard the time constraints so that the Lagrange multiplier is attributed to the budget constraint \(X^{s}=w_{s}\cdot h^{s}+\rho^{s}\). The first order conditions then write:
From \(\frac{\partial\mathcal{L}}{\partial h^{s}}\) and \(\frac{\partial\mathcal{L}}{\partial c^{s}}\) it follows that the disutility of one time-unit of paid labor is equal to that of one time-unit of child care, in the sense that both have an equal and negative impact on the remaining leisure time. Consequently, we have that \(-\lambda w_{s}=\frac{\partial U^{s}}{\partial H}\frac{\partial H}{\partial c^{s}}\) and so the marginal utility contribution of individual child care time equals the marginal utility contribution of labor time in the optimum. As such (and in our specific case of an interior solution) the exogenous individual wage rate determines both the optimal amount of working time and care time.
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Van Klaveren, C., Ghysels, J. Collective Labor Supply and Child Care Expenditures: Theory and Application. J Labor Res 33, 196–224 (2012). https://doi.org/10.1007/s12122-011-9127-4
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DOI: https://doi.org/10.1007/s12122-011-9127-4