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Who bears the full cost of children? Evidence from a collective demand system

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Abstract

This paper measures how the costs of children are shared between the father and the mother by estimating a gender-specific demand system related to the demand for market goods, household products and leisure within a collective approach. The estimates illustrate how the intra-household distribution of resources varies across households with and without children and how wages and non-labor income affect the allocation rule in both single-earner and double-earner households. In the presence of a child, both parents, but mothers especially, increase their involvement in home production at the expense of the enjoyment of leisure. This commitment decreases as the child gets older. In general, mothers control less than half of the household resources, while they bear more than half of the cost of maintaining a child.

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Notes

  1. Note that the household technology includes the full set of exogenous characteristics, while the utility function only hosts the demographic characteristics of the household members.

  2. The market approach is plausible when the domestic production is marketable, as it is the case of agricultural households or household–enterprises, or when it can be substituted with goods and services bought on an outside market at a given price. For example, meals can be taken at home or at a restaurant, a home-made cake has its perfect substitute in a pastry shop, a maid can be hired to clean the house, and so on. In this case, the market price of the equivalent service determines the trade-off between internal production and outside trade. This method requires a distinction between different types of domestic work and the evaluation of each one to the corresponding price of market specialists. Because information on the prices of specific household activities was not available, we could not apply this approach to our analysis.

  3. The superscript notation is associated with endogenous variables, while subscripts index exogenous variables.

  4. Because the level of the household product cannot be observed, the assumption of homotheticity (or constant return to scale) is a maintained hypothesis in collective models with household production (Apps and Rees 2002; Rapoport et al. 2011). See also Pollak and Watcher’s (1975) and Pollak (2011) discussion of the issue of constant return to scale in household production.

  5. Rapoport et al. (2011), in analogy with the distribution factors affecting the distribution rule but not preferences, term such production characteristics “pure production factors” because affect the production technology only, leaving preferences unchanged.

  6. It is interesting to note that the indirect utility function with a Gorman polar form implies a unitary model and the pooling of incomes because the aggregate demand behaves as if it were the demand of a single consumer (Bergstrom 1997:10). As pointed out by Bergstrom himself (1997: 10), in the case of a translation, utilities may be different for different people. The indirect utility described in Eq. (3) incorporates both translating and scaling of the income term.

  7. The functional form of the sharing rule is linear in the logarithms as it is implicitly assumed by Chiappori, Fortin and Lacroix (2002, eq. 10). Our functional form does not include interaction terms because not necessary for identification (Menon and Perali 2012) and implements the condition of income independence of the sharing rule also adopted by the identification strategy of Dunbar et al. (2013) and shown to be empirically robust in Menon et al. (2012).

  8. In the present context, the sharing rule can be thought as the analogous of a demographic function that instead of scaling prices as in the Barten (1964) tradition, scales income.

  9. Pollak and Wales (1979) show that equivalence scales suffer from a fundamental identification problem and criticize the possibility of meaningful welfare comparisons. For a recent discussion of these issues in the context of needs based equivalence scales, we refer to the paper by Menon and Perali (2010). Indifference scales introduced by Lewbel (2004) and later further developed also in Dunbar et al. (2013) and Browning et al. (2013) are defined as the lowest cost for, say, a woman living alone to attain the same indifference curve she attained living with the spouse. Indifference scales do solve the identification problem without having to resort to often-untestable assumptions regarding comparability of utility across individuals. Indeed, indifference scales implement interpersonal not inter-household comparisons and are not informative about the cost of children.

  10. See, for example, Apps and Rees (2002).

  11. The absence of comprehensive data sets including information about “who does what and when” and who consumes what in the family poses considerable challenges in terms of extra modeling effort and identifying assumptions. More comprehensive data are indeed to be collected, possibly within the same survey, to obtain more complete and robust answers to the research questions considered here.

  12. The linking procedure may modify the original properties of the source data sets. Because of imputation, measurement errors due to the exclusion of unmatched units or the erroneous match, or overrepresentation of matched units may arise and relevant information may be lost (Chesher and Nesheim 2006). Both the SHIW and the TBS contain information on socio-demographic characteristics of the households—such as household composition, age and level of education of each household member—which are relevant in explaining time use choices. Addabbo and Caiumi (2003) check whether the records drawn from the different data sources with reference to the selected household types, that is, couples with and without children, belong to the same population by testing the distance between different data sources.

  13. In particular, the matching procedure adopted in Addabbo and Caiumi (2003) can be illustrated as follows: To impute the variable of interest, \(y^{\prime }\), into the survey where it is unobserved, the authors take the conditional mean of the regression obtained from the survey where the \(y\) is observed, \({E}(y{\vert }{X}_{1})= \upbeta {X}_{1}\), and substitute the exogenous variables drawn from the survey where it is missing, \({X}_{0}\). The standard error of the regression is added, in order to reproduce as best as possible the unobserved heterogeneity not captured by the conditional mean of the regression. The variable of interest is then computed as \({y}^{\prime }=\upbeta {X}_{0}+\sigma _{\upvarepsilon }\). To test the matching procedure, the authors compare the estimated hours of work—devoted to child care, domestic activities and constrained time—and the observed data for the selected TBS subsample. They show that the simulated distribution is statistically close to the observed one on the basis of the first and second moments.

  14. It is worth noticing that this selection rule may generate a selection bias. However, our major concern was to maintain the comparability of our results with the original work by Apps and Rees. Non-participation, full or part time, is an extension of the collective model that has been treated in contexts without household production (Donni 2003; Blundell et al. 2007) only from a theoretical point of view. To the best of our knowledge, this important aspect has not been empirically implemented yet.

  15. Browning and Bonke (2009) distinguish three items categories: (a) assignable items because bought exclusively for one member, (b) assignable items because bought exclusively for the other member and (c) non-assignable items bought for the household such as food.

  16. We recognize that market wages for women fully employed in household production at best provide a lower bound to the real opportunity cost of their time. We thank a referee for this comment.

  17. As expected, we find that wages for females employed in the labor market, according to the same test, are exogenous.

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Acknowledgments

The authors wish to thank Maria Concetta Chiuri, Alessandro Cigno, Panayiota Lyssiotou, Martina Menon, Nathalie Picard, Ray Rees, Daniela Vuri and two anonymous referees for helpful comments. All errors and omissions are the authors’ own.

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Authors and Affiliations

  1. Econometric Studies and Forecasts Division, ISTAT - Italian National Institute of Statistics, Rome, Italy

    Antonella Caiumi

  2. Department of Economics, Università degli Studi di Verona, Vicolo Campofiore, 2, 37129, Verona, Italy

    Federico Perali

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  1. Antonella Caiumi
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  2. Federico Perali
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Correspondence to Federico Perali.

Appendix 1: Estimation results

Appendix 1: Estimation results

See Tables 8, 9 and 10

Table 8 Estimation of the potential wage equation for women
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Table 9 Estimation of gender-specific demand equations for non-traditional (double-earner) households
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Table 10 Estimation of gender-specific demand equations for traditional (single-earner) households
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Caiumi, A., Perali, F. Who bears the full cost of children? Evidence from a collective demand system. Empir Econ 49, 33–64 (2015). https://doi.org/10.1007/s00181-014-0854-2

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