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Market hours, household work, child care, and wage rates of partners: an empirical analysis

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Abstract

The aim of this paper is to provide new evidence on the effect of partners’ wages on partners’ allocation of time. Earlier studies concluded that wage rates are an important determinant of partners’ hours of market and non-market work and also that house work may lower married women’s wage rates. However, the bulk of earlier literature in this area failed to account for the endogeneity of wages or the simultaneity of partners’ time allocation choices. Here we take a reduced form approach and specify a ten simultaneous equations model of wage rates, employment and hours of market work, house work and childcare of parents. Non-participants are included in the model. We exploit a rich time use dataset for France to estimate the model. We find that the own wage affects positively own market hours and negatively own house work and childcare hours. The wage of the father has a significantly negative effect on the mother’s market hours while her wage rate has a significantly positive effect on his house work hours.

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Notes

  1. At the equilibrium value, where supply and demand meet, a marriage agreement will be reached.

  2. In terms of the solutions of the underlying structural model, the remainder includes leisure. Leisure is not modeled explicitly because of the adding-up condition built-in into the model: the total time allocated by each partner to the different activities considered cannot exceed 24 hours a day.

  3. See also Pollak (2005) for a discussion of the importance of using wage rates rather than earnings.

  4. To be more precise, combining the employment Eq. (3) with the paid work equations from (1) we have e ik  = 1, t * i1k  > 0 for the employed with a positive diary response for paid work and e ik  = 1, t * i1k  ≤ 0 for the employed with a zero diary response. For the nonemployed, we simply have e ik  = 0, as t i1k is not observed, and the underlying value could be either zero or positive.

  5. Since the seminal work of Blundell et al. (1998), it has become customary in the labor supply literature to identify the effect of wages on working hours by exploiting exogenous sources of variation in wages, due, for example, to law changes. Here, we do not have an exogenous source of variation at hand.

  6. However, one could argue that individuals choose their time allocation and their occupation together. Therefore, we re-estimate the model including occupational qualification dummies also in the time use equations (both including and excluding wages) and find that the coefficients are not statistically significant. Possibly because in France hours are quite strictly regulated and thus occupations do not drive working hours. Therefore, the empirical evidence supports our identification strategy.

  7. We do not use actual work experience as this is endogenous in our set up.

  8. Last, we need to assume that the wage equations, together with the selectivity into employment equations, can be used to recover the wage rates for the non-employed, for whom we do not observe wage rates. Flinn and Heckman (1982) address this recoverability problem in the context of a job search model and show that, in general, this requires parametric assumptions about the distribution of wage offers. The assumption of log-normally distributed wage rates is sufficient to pin down the wage rates for the non-employed.

  9. The French Time Use Surveys are carried out roughly every twelve years. The 2010 time use survey has been released to researchers only in July 2012 and amended a number of times, the last of which in April 2013. Moreover, in the 2010 Time Use survey a child was often required to fill in the diary with a parent, which makes the sample of couples in which both partners filled in the diary less than half the size of the one we are analyzing here.

  10. See, for example, Del Boca et al. (2007) on the effects of earnings and policies on fertility choices.

  11. We do not use region dummies as there are not enough observations for each of them (20).

  12. Burda et al. (2007) argue that men and women do the same total amount of paid and unpaid work.

  13. Notice, however, that Harley et al. 2012, argue that only the mean can be taken as representative of individual behaviour from cross-sectional diary data on a day time allocation.

  14. Although weekend work in France is becoming more and more common, it is still rare that both spouses may be employed in gainful employment on a weekend day, which makes the distinction between week and weekend days meaningful.

  15. We have computed the response of hours to a 1 % rise in wages. We simulated the model given by Eq. 1 1,000 times, using observed wages, whenever available, and simulated wages otherwise. To compute the elasticity of hours with respect to the husband (wife)’s wage, we increase all husbands (wives)’ wages by 1 % and simulate the model again. We thus record the change in time for each activity for both men and women and compute the elasticity. The procedure is repeated for non-labour income. The standard errors illustrate the variation in the elasticity which results from the use of parameter estimates. We also compute the impact of a change in wages on the total time allocated by spouses in each household on a given activity, by summing the husband’s and wife’s hours changes in each activity.

  16. Restricting the analysis to dual-earners, the wage of the husband shows a significant and negative effect on their wives’ domestic work hours. However, the cross-wage effect stays insignificant for child care hours of women. Restricting the sample to dual-earners, the positive effect of women’s wages on the hours of domestic work of their husband remains significant and increases substantially in size. The effect of her wage on his child care becomes insignificant, though it stays positive.

  17. However, since some of the components of non-labor income may depend on time allocation choices, we also experimented with dropping non-labor income from the model and our main conclusions were not affected (see Table 11).

  18. This is perhaps because employers expect young women to give birth and thus go on maternity leave.

  19. We define the summation ∑ 0 s=1 ≡ 0.

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Acknowledgments

This research has benefited from a grant by the French National Research Agency (ANR). Earlier versions of this paper were presented at the annual conference of the Society of Labor Economics, in Boston; and invited seminars at CREST Paris, RAND Santa Monica, University of the Philippines Baguio, Sciences-Po Paris, Cergy University; and at workshops held at Cergy University and at Nice University. We thank all seminars’ participants for their comments. We are especially indebted for helpful comments to Shoshana Grossbard, Almudena Sevilla-Sanz and the journal anonymous referees.

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Correspondence to Elena G. F. Stancanelli.

Appendix: Likelihood contributions

Appendix: Likelihood contributions

To deal with the multidimensional integration of the likelihood contributions, we estimate the model by simulated maximum likelihood, using the GHK algorithm (see, for instance, Börsch-Supan and Hajivassiliou 1993), proceeding as follows.

We write the variance-covariance matrix \(\Upsigma\) of the errors of the time-use, employment and wage equations as:

$$\Upsigma = \left( \begin{array}{ll} A & C' \\ C & \Upomega \end{array} \right)$$
(6)

with

$$\Upomega = Eu_i u_i', u_i = \left( \begin{array}{l} u_{im}\\ u_{if} \end{array} \right), C = E u_i \left( \begin{array}{l} \epsilon_{im}\\ \epsilon_{if}\\ \nu_{im}\\ \nu_{if} \end{array} \right)^{\prime},\; A = E \left( \begin{array}{l} \epsilon_{im}\\ \epsilon_{if}\\ \nu_{im}\\ \nu_{if} \end{array} \right) \left( \begin{array}{l} \epsilon_{im}\\ \epsilon_{if}\\ \nu_{im}\\ \nu_{if} \end{array} \right)^{\prime}$$
(7)

The joint density of the errors of the time-use equations (Eq. 1) and the employment equations (Eq. 3), conditional on the errors of the wage equations (Eq. 2), is normal with mean B i and variance-covariance matrix Z, with:

$$B_i = C'\Upomega^{-1}u_i, Z = A - C'\Upomega^{-1}C$$
(8)

Let L be the lower-triangular matrix implicitly defined by:

$$L L' = Z$$
(9)

with typical element l js j = 1, …8, s = 1, …, j. For each household, we draw R independent random numbers u * isr i = 1, …, Ns = 1, …, 7, r = 1, …, R from the uniform distribution over the range (0, 1). These random numbers are used to recursively simulate the likelihood contributions for the time-use equations of the husband, the time-use equations of the wife, and the employment equations of husband and wife. We initially assume that wages w im and w if are observed. Let l itmjr denote the simulated likelihood contribution for the j-th time use (j = 1, 2, 3) of the husband in household i, and replication r. If the husband reports no time spent on time use j  (j = 1, 2, 3), but is employed, we set Footnote 19

$$l_{itmjr} = \Upphi\left(- \frac{\alpha_{jm}^m \ln w_{im} + \alpha_{jm}^f \ln w_{if} + x_{im}'\beta_{jm} + \sum_{s=1}^{j-1}l_{js}\nu_{isr}} {l_{jj}} \right)$$
(10)

and

$$\nu_{ijr} = \Upphi^{-1}(l_{itmjr}u_{ijr}^*)$$
(11)

where \(\Upphi(.)\) represents the standard normal distribution function. If the husband is not employed, there is no information about the latent amount of paid work, because we do not know whether this state is due to choice or restriction, and the likelihood contribution is the probability (10) plus its complement, which leads to l itm1r  = 1 for paid work.

If the husband reports a positive amount of time spent on activity j, we set

$$l_{itmjr} = \frac{1}{l_{jj}} \phi\left( \frac{t_{ijm} - [\alpha_{jm}^m \ln w_{im} + \alpha_{jm}^f \ln w_{if} + x_{im}'\beta_{jm} + \sum_{s=1}^{j-1}l_{js}\nu_{isr}]} {l_{jj}} \right)$$
(12)

where ϕ(.) is the standard normal density function, and

$$\nu_{ijr} = \frac{t_{ijm} - [\alpha_{jm}^m \ln w_{im} + \alpha_{jm}^f \ln w_{if} + x_{im}'\beta_{jm} + \sum_{s=1}^{j-1}l_{js}\nu_{isr}]} {l_{jj}}$$
(13)

We take a similar approach for the time uses of the wife. If the wife reports no time spent on activity j, but she reports to be employed, we determine:

$$l_{itfjr} = \Upphi\left(- \frac{\alpha_{jf}^m \ln w_{im} + \alpha_{jf}^f \ln w_{if} + x_{if}'\beta_{jf} + \sum_{s=1}^{j+3-1}l_{js}\nu_{isr}} {l_{j+3,j+3}} \right)$$
(14)

and

$$\nu_{i,j+3,r} = \Upphi^{-1}(l_{itfjr}u_{i,j+3,r}^*)$$
(15)

If she is not employed, we have l itf1r  = 1 for her paid work.

If the wife reports a positive amount of time spent on activity j, we have l itfjr  = 

$$\frac{1}{l_{j+3,j+3}} \phi\left( \frac{t_{ijf} - [\alpha_{jf}^m \ln w_{im} + \alpha_{jf}^f \ln w_{if} + x_{if}'\beta_{jf} + \sum_{s=1}^{j+3-1}l_{js}\nu_{isr}]} {l_{j+3,j+3}} \right)$$
(16)

and

$$\nu_{i,j+3,r} = \frac{t_{ijf} - [\alpha_{jf}^m \ln w_{im} + \alpha_{jf}^f \ln w_{if} + x_{if}'\beta_{jf} + \sum_{s=1}^{j+3-1}l_{js}\nu_{isr}]} {l_{j+3,j+3}}$$
(17)

The likelihood contribution for the employment status of the husband, denoted by l iemr , is equal to, for a non-employed husband:

$$l_{iemr} = \Upphi\left( -\frac{q_{im}'\gamma_m + \sum_{s=1}^6 l_{7s}\nu_{isr}} {l_{77}} \right)$$
(18)

and

$$\nu_{i7r} = \Upphi^{-1}(l_{iemr}u_{i7r}^*)$$
(19)

For an employed husband, it is equal to:

$$l_{iemr} = 1 - \Upphi\left( -\frac{q_{im}'\gamma_m + \sum_{s=1}^6 l_{7s}\nu_{isr}} {l_{77}} \right)$$
(20)
$$\nu_{i7r} = \Upphi^{-1}((1 - l_{iemr}) + l_{iemr}u_{i7r}^*)$$
(21)

For the employment of the wife, we set the likelihood contribution l iefr if she is nonemployed equal to:

$$l_{iefr} = \Upphi\left( -\frac{q_{if}'\gamma_f + \sum_{s=1}^7 l_{8s}\nu_{isr}} {l_{88}} \right)$$
(22)

If she is employed, we set this equal to:

$$l_{iefr} = 1 - \Upphi\left( -\frac{q_{if}'\gamma_f + \sum_{s=1}^7 l_{8s}\nu_{isr}} {l_{88}} \right)$$
(23)

Next, we set the simulated likelihood contribution of household i, for replication r of the time-use equations and employment status equal to l ir , where

$$l_{ir} = \prod_{j=1}^3 l_{itmjr} l_{itfjr} l_{iemr} l_{iefr}$$
(24)

This is then averaged over replications to yield:

$$l_i = \frac{1}{R}\sum_{r=1}^R l_{ir}$$
(25)

In the empirical application we set R = 60.

Were neither the wage rates of the husband or the wife to be observed, before computing the above likelihood contributions we simulated their wages w imr and w ifr , by drawing them from their joint distribution, (defined by Eq. (2) and \(u_i \sim N(0,\Upomega)\)), and then plugged them into the simulated likelihood contributions listed above. If the wage rate of the husband is observed, but that of his wife is not, we draw the wife’s wage rate, w ifr , from the distribution of w if , conditional on w im , and plug it into the simulated likelihood contribution, as above. The likelihood contribution was completed by multiplying Eq. 25 by the marginal density of the husband’s wage rate. For households, where, on the contrary, the wife’s wage rate was observed but the husband’s was not, we proceed similarly. If both wage rates are observed, we multiply the simulated likelihood contribution Eq. 25 by the joint density function of the wife’s and husband’s wage rates.

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Bloemen, H.G., Stancanelli, E.G.F. Market hours, household work, child care, and wage rates of partners: an empirical analysis. Rev Econ Household 12, 51–81 (2014). https://doi.org/10.1007/s11150-013-9219-4

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