Skip to main content

Household production in a collective model: some new results


Household models estimated on labour supplies alone generally assume non-market time to be pure leisure. Previous work on collective household decision-making is extended here by taking domestic work into account in the Chiappori et al. (J Polit Econ 110(1):37–72, 2002) model. Derivatives of the household “sharing rule” can then be estimated in a similar way. Using the 1998 French Time-Use Survey, we compare estimates of labour supply functions assuming first that non-market time is pure leisure and then taking household production into account. The results are similar but more robust when household production is included. Collective rationality is rejected when domestic work is omitted.

This is a preview of subscription content, access via your institution.


  1. For a discussion of changes in female labor supply since the beginning of the twentieth century, see Marchand and Thelot (1991) and Sofer (2005).

  2. As shown in Apps and Rees (1996).

  3. Examples include the models in Apps and Rees (1996, 2002), Couprie (2007), and, for a mainly empirical approach Aronsson et al. (2001).

  4. The INSEE (Institut National de la Statistique et des Etudes Economiques) is the French Institute for Statistics and Economic Studies. We are grateful to the French Research Center LASMAS for making the data available to us.

  5. See also Samuelson (1956).

  6. As originally introduced in bargaining models by Manser and Brown (1980) and McElroy (1990).

  7. As in the farm production model of the development literature.

  8. This could be questionable for activities which have a strong component of leisure or “own” consumption, such as time spent playing with children or cooking for friends. In these cases, there is joint production (see Pollak and Wachter 1975). However, activities of this kind represent only a small proportion of total household “tasks”.

  9. See, for example, Lacroix et al. (1998).

  10. In France, an exception is the 1989 Modes de Vie survey, but it suffers from important drawbacks for our purpose (see Lecocq 2001).

  11. As in Gronau (1977).

  12. It can be argued that both market and domestic goods may have a public component. A few papers deal with public goods besides private consumption (see, for example, Chiappori et al. 2005 or Donni 2006), but they do not include domestic production. Couprie (2007) assumes that market goods are privately consumed, and only domestic goods are assumed to be public goods.

  13. Here, the weights are a function of prices, among other variables.

  14. More specific assumptions about household production functions may of course lead to interesting results, as in Donni (2008) and in Rapoport and Sofer (2004) where specifying a CES production function permits the derivation of results for the case of non-marketable household goods.

  15. From the proof in Appendix 1

  16. An exception is Bourguignon and Chiuri (2005).

  17. We also tried using annual working hours, as in Chiappori et al. (2002). The results, which are not reported here, are very similar to those from model 1.

  18. Non-labour income is known only at the household level (not at the individual level). Also, for some households, only labour income brackets are known. For these households, labour income was estimated using a larger survey from the INSEE (“Enquête sur l’emploi 1999”, i.e. Labour Force Survey 1999). All the information about the estimations is available from the authors.

  19. See last line of Table 2.

  20. France is divided into 100 areas called departments.

  21. See Appendix 1.


  • Apps PF, Rees R (1988) Taxation and the household. J Public Econ 35(3):355–369

    Article  Google Scholar 

  • Apps PF, Rees R (1996) Labour supply, household production and intra family welfare distribution. J Public Econ 60(2):199–220

    Article  Google Scholar 

  • Apps PF, Rees R (1997) Collective labor supply and household production. J Polit Econ 105(1):178–190

    Article  Google Scholar 

  • Apps PF, Rees R (2002) Household production, full consumption and the costs of children. Labour Econ 8(6):621–648

    Article  Google Scholar 

  • Aronsson T, Daunfeldt SO, Wikström M (2001) Estimating intra-household allocation in a collective model with household production. J Popul Econ 14(4):569–584

    Article  Google Scholar 

  • Bourguignon F, Chiuri MC (2005) Labour market time and home production: a new test for collective models of intra-household allocation. Centre for Studies in Economics and Finance (CSEF) Working Paper 131, University of Naples

  • Chiappori PA (1992) Collective labor supply and welfare. J Polit Econ 100(3):437–467

    Article  Google Scholar 

  • Chiappori PA (1997) Introducing household production in collective models of labor supply. J Polit Econ 105(1):191–209

    Article  Google Scholar 

  • Chiappori PA (1998) Rational household labor supply. Econometrica 56(1):63–89

    Article  Google Scholar 

  • Chiappori PA, Fortin B, Lacroix G (2002) Marriage market, divorce legislation and household labor supply. J Polit Econ 110(1):37–72

    Article  Google Scholar 

  • Chiappori PA, Blundell R, Meghir C (2005) Collective labor supply with children. J Polit Econ 113(6):1277–1306

    Article  Google Scholar 

  • Couprie H (2007) Time allocation within the family: welfare implications of life in a couple. Econ J 117(516):287–305

    Article  Google Scholar 

  • Donni O (2006) The intrahousehold allocation of private and public consumption: theory and evidence from US data. IZA Discussion Papers 2137, Institute for the Study of Labor

  • Donni O (2008) Labor supply, home production, and welfare comparisons. J Public Econ 92(7):1720–1737

    Article  Google Scholar 

  • Fortin B, Lacroix G (1997) A test of the unitary and collective models of household labour supply. Econ J 107(443):933–955

    Article  Google Scholar 

  • Goldschmidt-Clermont L, Pagnossin-Aligisakis E (1995) Measures of unrecorded economic activities in fourteen countries. In: UN Development Report Office Occasional Paper 20, New York, pp 105–155

  • Gronau R (1977) Leisure, home production and work—the theory of allocation of time revisited. J Polit Econ 85(6):1099–1123

    Article  Google Scholar 

  • Lacroix G, Picot M, Sofer C (1998) The extent of labour specialization in the extended family: a theoretical and empirical analysis. J Popul Econ 11(1):223–237

    Article  Google Scholar 

  • Lecocq S (2001) The allocation of time and goods in household activities: a test of separability. J Popul Econ 14(4):585–597

    Article  Google Scholar 

  • Manser M, Brown M (1980) Marriage and household decision making: a bargaining analysis. Int Econ Rev 21(1):31–44

    Article  Google Scholar 

  • Marchand O, Thelot C (1991) Deux siècles de travail en France. INSEE, Paris

    Google Scholar 

  • McElroy MB (1990) The empirical content of Nash-bargaining household behavior. J Hum Resour 25(4):559–583

    Article  Google Scholar 

  • Pollak RA, Wachter ML (1975) The relevance of the household production function and its implications for the allocation of time. J Polit Econ 83(2):255–77

    Article  Google Scholar 

  • Rapoport B, Sofer C (2004) Pure production factors and the sharing rule: estimating collective models with household production. Working Paper MSE, Université Paris1-Panthéon-Sorbonne

  • Rizavi SS, Sofer C (2008) The division of labour within the household: is there any escape from traditional gender roles? Working paper, University Paris1

  • Robinson JP, Chenu A, Alvarez AS (2002) Measuring the complexity of hours at work: the weekly work grid. Mon Labor Rev 125(4):44–54

    Google Scholar 

  • Samuelson PA (1956) Social indifference curves. Q J Econ 70(1):1–22

    Article  Google Scholar 

  • Sofer C (1999) Modélisation économique de la prise de décision dans la famille. In: Majnoni d’Intignano B (ed) Egalité entre femmes et hommes: aspects économiques. Conseil d’Analyse Economique, La Documentation Française, Paris

  • Sofer C (2005) La croissance de l’activité féminine. In: Maruani M (ed) Femmes, genre et sociétés: l’ état des savoirs. La Découverte, Paris, pp 218–226

    Google Scholar 

Download references


We would like to thank Andrew Clark (Paris-Sciences Economiques), Olivier Donni (Université de Cergy) and Guy Lacroix (Université Laval) for helpful comments. We are also grateful to Alessandro Cigno, the editor, as well as to the two anonymous referees for their very valuable comments and suggestions.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Catherine Sofer.

Additional information

Responsible editor: Alessandro Cigno


Appendix 1: Proof of Proposition 1

Recall that ψ = ψ f . We also have: \(\psi _m =\mathit\Pi +y-\psi \)

By differentiation of the labour supply equations

$$ \label{eq17} h^f=L^f\left( {\it{w}_f ,\psi \left( {\it{w}_f ,\it{w}_m ,y,...s_l ...;{\rm {\bf z}}} \right);{\rm {\bf z}}} \right) $$
$$ \label{eq18} h^m=L^m\left( {\it{w}_m ,\mathit\Pi \left( {\it{w}_f ,\it{w}_m ;{\rm {\bf c}},{\rm {\bf z}}} \right)+y-\psi \left( {\it{w}_f ,\it{w}_m ,y,...s_l ...;{\rm {\bf z}}} \right);{\rm {\bf z}}} \right) $$

we obtain:

$$ \label{eq19} \frac{\partial h^f}{\partial \it{w}_m }=\frac{\partial L^f}{\partial \psi }\frac{\partial \psi }{\partial \it{w}_m } $$
$$ \label{eq20} \frac{\partial h^m}{\partial \it{w}_f }=\frac{\partial L^m}{\partial \psi _m }\left( {\frac{\partial \mathit\Pi }{\partial \it{w}_f }-\frac{\partial \psi }{\partial \it{w}_f }} \right) $$
$$ \label{eq21} \frac{\partial h^f}{\partial \it{w}_f }=\frac{\partial L^f}{\partial \it{w}^f}+\frac{\partial L^f}{\partial \psi }\frac{\partial \psi }{\partial \it{w}_f } $$
$$ \label{eq22} \frac{\partial h^m}{\partial \it{w}_m }=\frac{\partial L^m}{\partial \it{w}^m}+\frac{\partial L^m}{\partial \psi _m }\left( {\frac{\partial \mathit\Pi }{\partial \it{w}_f }-\frac{\partial \psi }{\partial \it{w}_m }} \right) $$
$$ \label{eq23} \frac{\partial h^f}{\partial y}=\frac{\partial L^f}{\partial \psi }\frac{\partial \psi }{\partial y} $$
$$ \label{eq24} \frac{\partial h^m}{\partial y}=\frac{\partial L^m}{\partial \psi _m }\left( {1-\frac{\partial \psi }{\partial y}} \right) $$
$$ \label{eq25} \frac{\partial h^f}{\partial s_l }=\frac{\partial L^f}{\partial \psi }\frac{\partial \psi }{\partial s_l } $$
$$ \label{eq26} \frac{\partial h^m}{\partial s_l }=\frac{\partial L^m}{\partial \psi _m }\left( {-\frac{\partial \psi }{\partial s_l }} \right) $$

Note that, with reference to the results in Chiappori et al. (2002), only Eqs. 19 and 20 include a new specific term: \(\frac{\partial \mathit\Pi }{\partial \it{w}_f }\)

Taking the same notation, we define \(A=\frac{h_{\it{w}_m }^f }{h_y^f }\), \(B=\frac{h_{\it{w}_f }^m }{h_y^m }\), \(C_l =\frac{h_{s_l }^f }{h_y^f }\), \(D_l =\frac{h_{s_l }^m }{h_y^m }\). We assume only one distribution factor and suppress the subscripts l and q to simplify the notation. The partial derivatives of the sharing rule with respect to wages, non-labour income and the distribution factor are given by:

\(\frac{\partial \psi }{\partial y}=\frac{D}{D-C}; \quad \frac{\partial \psi }{\partial s}=\frac{CD}{D-C}; \quad \frac{\partial \psi }{\partial \it{w}_m }=\frac{AD}{D-C}.\) Only \(\frac{\partial \psi }{\partial \it{w}_f }\) is modified. From Hotelling’s lemma, we obtain: \(\frac{\partial \mathit\Pi }{\partial \it{w}_f }=-t_f \), and then \(\frac{\partial \psi }{\partial \it{w}_f }\) is given by:

\(\frac{\partial \psi }{\partial \it{w}_f }=\frac{BC}{D-C}-t_f .\) Note that t f is fully observed in the data.

The same result holds with several distribution factors. This is a straightforward result from Chiappori et al. (2002). Note also that when there is more than one distribution factor, testable restrictions similar to those presented in Chiappori et al. (2002) can be derived from the model.

Finally, with no domestic production, the model simplifies to \(\mathit\Pi \) = 0, and thus \(\frac{\partial \mathit\Pi }{\partial \it{w}_f }=0\), and ψ is now simply non-labour income. In this case, Eq. 20 reduces to:

$$ \frac{\partial h^m}{\partial \it{w}_f }=\frac{\partial L^m}{\partial \psi _m }\left( {-\frac{\partial \psi }{\partial \it{w}_f }} \right) $$

and (4) to:

$$ \frac{\partial h^m}{\partial \it{w}_m }=\frac{\partial L^m}{\partial \it{w}^m}+\frac{\partial L^m}{\partial \psi _m }\left( {-\frac{\partial \psi }{\partial \it{w}_m }} \right) $$

Then, \(\frac{\partial \psi }{\partial \it{w}_f }\) reduces to:

$$ \frac{\partial \psi }{\partial \it{w}_f }=\frac{BC}{D-C} $$

And thus the formulas in Chiappori et al. (2002) are found as a special case of the more general model developed here.

Appendix 2: Description of domestic tasks

Domestic activities include all activities around:

  • food and drink: preparation (cutting, cooking, making jam), presentation (laying the table), kitchen and food clean-up (washing up)

  • housework: interior cleaning, clothes activities (laundry, mending, sewing, knitting, repairing and maintaining textiles), storing interior household items and tidying

  • interior maintenance and repair of house and vehicles: repairing, water and heating upkeep

  • household management: financial (bills, count,...)

  • shopping

  • childcare: physical and medical care, reading, talking with and listening to children, homework help, picking up/dropping off children, playing and leisure with children

  • care for household adults

  • care for animals and pets

  • lawn, garden and houseplants

Appendix 3: Computation of the male’s share

In Table 4, the derivatives of the sharing rule have been computed directly calculating the derivatives of \(\mathit\Pi +y-\psi \) using formulas symmetrical to those which appear in Section 3.3.

The formulas in Appendix Appendix 1: Proof of Proposition 11 show that the derivatives of the sharing rules are not symmetrical for the man and the woman, because of the term t f in the derivative with respect to \(\it{w}_{f}\). It thus must be checked whether the results are the same when computing directly the derivatives of the male’s share. In this latter case, ψ represents now the man’s share and \(\mathit\Pi +y-\psi \) the woman’s share.

As the reduced forms of labour supply are identical, we expect the derivatives with respect to the male and female wages to have an opposite sign and to be about the same absolute value in Table 3. The same should hold for the derivative with respect to the sex-ratio (the coefficient is in fact the exact opposite, see Table 3). The derivative with respect to non-labour income is the complement to 1 of the coefficient computed in Table 3; indeed, we exchange ψ and \(\mathit\Pi +y-\psi \), so that we exchange and as \(\mathit\Pi \) does not depend on y.

Table 4 presents the results. When comparing with the results of model 2b in Table 3, it can be seen that the derivatives relative to wages show, as expected, an opposite sign and a similar value: an increase in either the male or the female wage should have an exact opposite effect on the male and the female income share. The same expected result is observed for the sex ratio, where the parameters obtained in the two models are exactly opposite and both significant. As expected also the coefficient found for non labour income is the complement to 1 for the coefficient found in the case of the female’s share: when non labour income increases, say by one euro, then it was found (Table 3) that the female share increased by about 62 cents. Here, it is found that the male share does increase in that case by 1–62 cents = 38 cents. For this coefficient, χ 2 tests show that on one hand, we cannot reject the null-hypothesis, but on the other hand, the hypothesis that it equals to 1 can be rejected (these are the exact symmetries of the results found in Table 3).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Rapoport, B., Sofer, C. & Solaz, A. Household production in a collective model: some new results. J Popul Econ 24, 23–45 (2011).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Collective model
  • Household production
  • Labour supply

JEL Classification

  • D13
  • J22