Poverty and inequality within Brazilian households: an application of a collective consumption model

According to De Souza (2012, p. 7), Brazil’s GINI Index of the household per capita income has slowly decreased from 0.594 in 2001 to 0.539 in 2009 indicating a rather significant problem of income disparity. Regarding poverty, from 2004 to 2009 the share of the population with less than a minimum wage per month decreased from 71 to 58%, yet in 2009 the extremely poor accounted for 4.7% of the population and the poor came to almost 9.4% of Brazilians and people vulnerable to poverty amounted to around 44% of the total population (Osorio et al. 2011). More recent figures indicate that, in 2014, the Brazil’s GINI Index was 0.494, and the rates of extreme poverty and poverty were 2.8% and 7.3% of the population, respectively (see Brazil 2015).

Traditionally, microeconomic theory considers households as single decision-making units. This so-called unitary model only considers allocation among households and disregards questions concerning individual preferences and intra-household inequalities, which may lead to wrong welfare implications (Haddad and Kanbur 1990, 1992). Unitary model has been criticized both from a theoretical and an empirical perspective by several authors who have developed alternatives termed as collective approaches to household behavior (Bourguignon and Chiappori 1992).

The collective models of household consumption are those in which the household is described as a group of individuals, each of whom is characterized by particular preferences, and among whom intra-household bargaining and collective decision processes are assumed to take place (Vermeulen 2002). The only assumption about the decision process is that it is efficient. According to Xu (2007, p. 3), the collective framework explains phenomena that cannot be understood under the unitary approach and it reshapes policy instruments to make social welfare and individual development programs more efficient.

As clearly explained in Bargain et al. (2014), the Rothbarth approach “… is a method that allows retrieving how household resources are allocated between parents and children. It consists in examining the extent to which the presence of children depresses the household consumption of adult-specific goods” (see, particularly, p. 262, and the references therein).

See Deaton (1989, 1997), Rose (1999), and Dunbar et al. (2013) for recent discussions.

Joint consumption is the shared use of commodities in multi-person households, i.e., collective enjoyment of goods, like housing, television, fridge, or utilities, which are in the nature of ‘public goods’ to the family and by which ‘scale economies’ take place. In family economics, household consumption can be divided into private or collective (public) depending on the type of good being shared among the household members. This applies to household goods such as furniture, housing, family car, home heating/cooling, etc.

An indifference scale is a scalar that equates the utility of a person living alone to the utility of the same individual if he or she lived with a partner. More generally, an indifference scale represents the income adjustment applied to person when living in a multi-person household (with or without children) for her/him to reach the same indifference curve as when living alone.

In the literature on equivalence scales, this restriction that resource shares are independent of expenditure is known as ‘independent of base’ (IB) scaling of consumption (Blackorby and Donaldson 1993; Lewbel 1991). IB is a function, independent of total expenditure—and, hence, of the utility level—at which it is evaluated, which scales the expenditure of each individual in the household and represents the economies from joint consumption (Lewbel and Pendakur 2008; Bargain et al. 2014).

See Bargain and Donni (2012a) and Lewbel and Pendakur (2008) for recent discussions in detail on this intuition.

The price elasticity \( \varepsilon_{i,n}^{k} \) is a translation function specific to good k and it is related to the differences that may exist between goods with respect to the possibility of joint consumption. Bargain and Donni (2012a, p. 797) point out that scale economies may have a wealth effect and a substitution effect represented by logs_i,n and \( \varepsilon_{i,n}^{k} \), respectively. This latter effect can be positive or negative depending on the nature of good k, i.e., if good k is essentially public or private.

The level of joint consumption depends on the nature of the good, i.e., if the good is completely private or if it has a public component. We assume that the proportion of goods consumed jointly within the household is constant (σ) but not the same for all household members. For example, the consumption of member i = m, w in a household with n ≥ 2 is extended by a fraction of joint consumption of the other household members:

so, after some convenient simplifications, we have σ = [η_i,n(z)·(1 − s_i,n(z))]/[s_i,n(z)·(1 − η_i,n(z))] which is a normalized indicator of individual economies of scale for each household member that compares the level of the scale s_i,n(z) to the level of the corresponding share η_i,n(z).

In POF of 2008–2009, children’s clothing expenditures are defined as the acquisition and rental of children’s clothing up to 14 years (IBGE 2010a).

This selection can potentially distort our measures of poverty. However, we have some reasons to believe that our results will not be significantly affected. Indeed, the aggregate poverty rate at the level of our study sample using a traditional poverty line (the exact definition of which is given below) amounts to 5.7%, which is of the same order of magnitude as the poverty rate in the extended sample including all family types (8.7%). Of course, our results could still be misleading if the distribution of resources among selected households is very different compared to the rest of the population.

We have decided to exclude the budget share “household operations” from the system of equations for at least two reasons. First, it is traditionally recognized in the household behavior analysis that housing expenses may be difficult to evaluate for homeowners and thus these expenditures are not well captured so they are not typically modeled (Bargain and Donni 2012a; Bargain et al. 2014). Second, we have to acknowledge that the size of the household may be highly correlated with (and thus endogenous in making) housing decisions. Moreover, these housing expenditures are usually considered long-term decisions and depend more on permanent than on annual income (Kain and Quigley 1972). However, when household economies of scale are considered, as in our analysis of individual poverty, expenditures on housing cannot be omitted at all (Bargain et al. 2014). Later in this paper, we take into account a variation of the initial model with the inclusion of household operations to see the importance of their “public good” component or their role in the economies of scale within the household and to check the robustness of our results.

The model allows testing the hypothesis that preferences over consumption are stable. For this, we perform a simple Breusch–Pagan test for independent equations. The Breusch–Pagan statistic for independence, which follows a Chi-squared distribution under the null hypothesis, is about to 33,015. The null hypothesis is then rejected at the 1% level. Thus, the assumption that the parameters for singles and couples are the same seems to be a reasonable approximation.

We implement a simple test for the IB restriction, following closely Menon et al. (2012, p. 741). In particular, we pool all the household sizes, which would give a test with more statistical power, and estimate coefficients from regressions of each individual resource share on a linear and quadratic models in expenditure which include a categorical variable for each household size and dummies for each federal unit of residence. The results indicate that none of the log expenditure is individually statistically significant. This suggests that the hypothesis that resource shares do not vary with expenditure is not violated in these data and thus that identification of resource shares on the basis of IB restriction is valid.

The presence of child gender bias in these latter studies might be attributed to cultural aspects of such countries. On the other hand, evidence of gender discrimination among children in developing countries often pertains to long-term expenditure on children, especially ‘productive’ investments on children’s education and health (Sen 1981). However, the literature on differences in education and health expenditures is extensive and beyond the scope of our study.

The per capita measures do not overstate child poverty for the case of couples with three children.