On December 5 and 6, the PoRESP team, together with Bram De Rock (ULB) and William Pariente (UCL, IRES) organized the conference “Poverty and the Family”, in Brussels.
All presented papers shared one important belief: families do not behave as a single individual. Quite the contrary, household decisions are the result of a collective decision process, involving different individuals, characterized by potentially different preferences and different bargaining power over the decision process. This view has important consequences: while the economic theory focuses on individual welfare, but data is only available at the household level, so we need a way to retrieve individual welfare from outcomes measured at the household level – and there, assumptions on intrahousehold decision making play a key role.
Let’s now focus on consumption: we would like to measure individual consumption based on the data on household consumption. In order to get individual consumption from household consumption, we need to deal with two problems: first, resources are likely to be unequally shared within the household. Second, members of the household share (at least partly) some goods (heating, car). The traditional way to deal with shared goods is to use equivalent scales, which correct for the fact that a household need less resources when living together than what its members would need living apart.
Allowing the household to be a collection of different individuals has two major consequences for the economics of poverty, both discussed in the conference. First, wellbeing and resources are likely to be unevenly distributed within the household. By using equivalence scales to compare households of different sizes, classic welfare analysis makes the underlying assumption that wellbeing is evenly distributed within households. This is likely to give a wrong picture of inequalities between individuals (as explained here) and of poverty rates (see here).
Second, the intra-household decision process might have some consequences on the outcome of the household decision, especially on the provision of goods held by the family that can be commonly used by its members (hence, having a public good character at the household level), thus on individual welfare. On the one hand, cooperative models of household state that whatever the decision process households make efficient decisions. On the other hand, non-cooperative models of households take into account the possibility of reaching a non-efficient outcome.
In the following of this post, I’m going to focus on the distribution of resources within household.
Let’s take two individuals living together, and imagine they consume a bundle of goods of value X (total expenditure). They are different from each other in terms of preferences and bargaining power. Still, they take together the decision over the way they purchase the bundle of goods, but the decision is influenced by the bargaining power. The higher the bargaining power one has, the more she influences the consumption choices. Under the assumption that the two individuals take efficient decisions, the second fundamental theorem states that the outcome of the household decision can be reached with a (theoretical) two-step procedure: first, individuals share their resources, second, they individually choose the bundle of goods they want to purchase. A key feature of this way of presenting the decision process is that it allows defining the sharing rule. The sharing rule is the way resources are shared in the first step. It is directly related to the bargaining power: the higher the bargaining power one has, the higher the share one gets. Both the sharing rule and the bargaining power can be influenced by other factors: market prices, total expenditure, distribution factors: they are variables that affect bargaining power, but do not affect preferences for goods and services such as divorce laws or ratio of males over females.
Being able to measure the sharing rule is absolutely key to draw conclusions on inequalities and poverty: you would not draw the same conclusion on inequalities between individuals if both partners get 50% of expenditures than if one get 75% and the other 25% in all couples. But the main problem we face is that the sharing rule CANNOT be measured – in econometric terms: it is not identified – except under some additional assumptions and/or additional information. And, as presented by Arthur Lewbel, this is where research stands: defining the assumptions and the required information under which we are able to measure the sharing rule.
In a nutshell, in order to recover the sharing rule, one can adopt two strategies. First strategy, she would need to impose some additional assumptions on the comparison of preferences between individuals over different household structures. But additional assumptions on preferences are not very appealing (e.g. singles might have different preferences than spouses) and it raises new deep questions on the formation of preferences, such as: do preferences change in marriage? Second strategy, she would need additional information, such as the existence of distribution factors, as in the paper presented by Krishna Pendakur).But distribution factors are very rare variables, it is sometimes possible to observe one and almost impossible to observe two of them (the paper presented by Valérie Lechene is a unique case). Nevertheless, Frederic Vermeulen showed that although the sharing rule cannot be measured, it is always possible to measure bounds on the sharing rule. That is, instead of giving precisely that a member gets 45% of ressources, it is possible that it gets between 41% and 49% (41, 45 and 49% are invented figures for the sake of the post) (Cherchye et al., 2013).
Therefore, the literature is making great progress in the measure of intrahousehold inequalities. However, is the measure of the sharing rule sufficient to draw welfare conclusions at the individual level? Following the definition of indifference scales proposed by Browning, Chiappori, Lewbel (2013), an appealing alternative would be to compute the income one requires to be as well-off when living alone (and thus, without benefiting from the fact that the consumption of some goods such as heating can be shared within the household i.e. without benefitting from economies of scale) than living in a multi-persons household (and thus benefiting from economies of scale). But what does “as well-off” mean? Information on the share of resources two individuals get is not sufficient to tell if they are equally well-off: we need to know how they value it! In other terms, we need to know what their preferences are. Therefore, the estimation of indifference scales is more demanding than the estimation of the sharing rule.
To conclude, the conference has been a good opportunity to gauge the great advances the literature made in the last few years and it paved the way to new exciting research questions!
APPENDIX: more technical details on the presentations
The sharing rule is a key ingredient for any individual welfare analysis. Though, its identification is not a piece of cake. Arthur Lewbel presented an overview (Lewbel et al., 2013) on the different methods to identify the sharing rule. Generation 1 models showed that the level of the sharing rule is not identified, but the variations are (the identification results are given by Chiappori and Ekeland, 2009). However, identifying variations of the sharing rule is not sufficient for welfare analysis: we need to know how much males and females get on average, and not only that this share is affected by some factors, such as the difference of ages between spouses. Generation 2 models show that the level of the sharing rule is uniquely identified only under some additional assumptions (comparison of preferences between individuals over different household structures) or additional information (such as the existence of distribution factors as in the paper presented by Krishna Pendakur (Dunbar et al., 2013)). The main problem of those methods is that additional assumptions on preferences are not very appealing (e.g. singles might have different preferences than spouses) and additional information is not always available. Indeed, comparison of preferences raise new open questions such as: do preferences change in marriage? Nevertheless, Frederic Vermeulen showed that it is possible to identify bounds on the sharing rules, without any additional assumption or information by applying revealed preference restrictions (Cherchye et al., 2013). The bounds appear to be pretty informative. The identification of the level of the sharing rule is therefore at the frontier of research.
Dunbar et al. (2013) show that the level of the sharing rule can be recovered using distribution factors, providing that it does not depend on total expenditure i.e. the share one gets in the household does not depend on how much the household consumes (but they allow it to depend on closely related factors such as wealth). This assumption is not testable in their framework and key for the identification. They illustrate their method investigating the effect of access to credit on within-household allocation consumption in Malawi. They show that the effect of credit on resource shares members of the household get crucially depends on the type of credit: microcredit and agriculture credit tend to divert resources from children, and also on who receives the credit: credit attributed to women tend to divert resources from men to children and women.
The crucial assumption here is that resource shares do not depend on total expenditure. The method proposed by Cherchye et al. (2013) permits to test this assumption. They provide a surprising result, namely that resource shares do not depend on household full-income, defined as the sum of both spouses maximum possible labor income and nonlabor income (excluding savings and expenditures on durables). Though, their definition of full income is slightly different from total expenditure, as it takes into account leisure.
However, is the identification of the sharing rule sufficient to draw welfare conclusions at the individual level? Cherchye et al. (2013) base their poverty analysis on the share of full-income an individual gets. However, following the definition of indifference scales proposed by Browning, Chiappori, Lewbel (2013), an appealing alternative would be to compute the income one requires to be as well-off living when living alone (and thus, without benefiting from the fact that the consumption of some goods such as heating can be shared within the household i.e. without benefitting from economies of scale) than living in a multi-persons household (and thus benefiting from economies of scale). Therefore, the estimation of indifference scales is more demanding than the estimation of the sharing rule, as it also requires to measure economies of scale and preferences of individuals.
 Let me here introduce a piece of definition. I often use “family” and “household” as if they were recovering the same idea. However, “household” refers to the idea of a group of individuals living together, whereas “family” can either refer to the nuclear family or the extended family. So, a household can be composed of different families, while a family can be decomposed into different households. Most of studies to which I refer here are about intrahousehold decision making, except when explicitly specified. We are often interested in household because it is the most common unit of observation in survey: most data on consumption and wealth are observed at the household level, and not at the individual level, yet we want to draw conclusions at the individual level. Moreover, it is very likely that some decisions observed at the individual level results from the household decision, such as labor supply of women.
 Pierre-André Chiappori and Ivar Ekeland, 2009 “The Microeconomics of Efficient Group Behavior: Identification,” Econometrica, Econometric Society, vol. 77(3), pages 763-799, 05.
 Arthur Lewbel “Identifying sharing rules in collective households models – An overview”, talk given at the PoRESP conference “Poverty and the Family”, Dec. 5, 2013 (coauthors: Krishna Pendakur, Geoffrey Dunbar, Martin Browning, Pierre-André Chiappori, Laurens Cherchye, Bram De Rock, and Frederic Vermeulen)
 Krishna Pendakur “Identification of random resource shares in collective households with an application to credit in Malawi” talk given at the PoRESP conference “Poverty and the Family”, Dec. 6, 2013 (coauthors: Geoffrey R. Dunbar, Arthur Lewbel)
 Valérie Lechene presented a paper (Orazio Attanasio and Valerie Lechene “Efficient responses to targeted cash transfers” forthcoming, October 2013, Journal of Political Economy) in which they identify two distribution factors, i.e. two observed variables that influence the bargaining power of spouses without impact preferences: they use the randomization setting of the conditional cash transfer PROGRESA targeting poor households in Mexico (as it is randomly assigned, receiving the transfer is not associated with preferences of agents) and the family network of spouses as distribution factors. This setting allows them to test collective rationality. Observing one good distribution factor is obviously difficult, observing two distribution factors, such as this paper does, is a unique case.
 Laurens Cherchye, Bram De Rock, Arthur Lewbel and Frederic Vermeulen, 2013 “Sharing Rule Identification for General Collective Consumption Models,”
 Martin Browning, Pierre-André Chiappori and Arthur Lewbel, 2013.”Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power,” Review of Economic Studies, Oxford University Press, vol. 80(4), pages 1267-1303.