Abstract This paper applies recent developments in collective model estimation to elicit the allocation of resources in African families in South Africa. We use the 2010/11 South African Income and Expenditure Survey as it contains exclusive goods, i.e., goods consumed by specific household members, to be used for identification. We rely on a consumption model that accounts for (potentially unequal) resource sharing and jointness in consumption (generating economies of scale). Results indicate that men tend to receive more than women (even if imprecise estimates make the difference statistically insignificant), leading to sharp gender differences in terms of poverty. Ignoring economies of scale leads to an overestimation of poverty among adult men and women living with others. Children’s resource shares are in line with international standards but household resources are relatively low among African families so that ignoring intrahousehold allocation leads to an underestimation of child poverty. 1. Introduction Empowering women for economic development has always been high on the post-apartheid South African government’s transformative agenda. This has been actioned through a myriad of nationwide measures, e.g., integrating women into the education system and into economic activities, and instituting pro-gender equity legislation. Regardless, women still fare worse than men in attributes of welfare enhancement (Hoogeveen and Ozler, 2005; Leite et al., 2006; Leibbrandt et al., 2012). This begs the question whether the low sensitivity of gender equity to state interventions is partly sparked by household members’ perspectives on gender equity in general and, precisely, on the effective allocation of resources within households. For South Africa, the gender equity dimension in resource allocation at household level has received limited attention so far (among exceptions are Duflo, 2000; Case, 2002; Wittenberg, 2009; Kreuser, 2013). The present paper suggests new evidence based on structural estimations. Traditionally, it has been assumed that resources are allocated equitably, or according to needs, among household members, notably in the unitary model of Becker (1981). The development of collective models has allowed putting a formal structure on the potentially unequal allocation of resources within the household (Chiappori, 1988, 1992). At the same time, the theory underlying the unitary model, notably the absence of individualism, has been criticised while empirical evidence has led to a clear rejection of this model when applied to couple data (Browning and Chiappori, 1998), as well as the rejection of necessary conditions like the income pooling hypothesis (Lundberg et al., 1997). It has been suggested that the distribution of resources in the household depends on the control over external streams of income (Bourguignon et al., 2009), policies affecting outside options (Alderman et al., 1995) and more generally the ‘distribution factors’ that influence the sharing rule (Chiappori et al., 2002). Strikingly, the collective model has become operational only recently. Indeed, most of the early literature following Chiappori (1988, 1992) has consisted in testing the efficiency assumption at the core of this theory (e.g., Bourguignon et al., 2009) or in identifying the marginal sharing rule (e.g., Browning et al., 1994). Only recently has the complete resource allocation between spouses been identified under some assumptions about preference stability across family status (Browning et al., 2013). This approach, at the core of the present study, represents a valuable extension of the Rothbarth (1943) approach, notably as it additionally accounts for economies of scale and parental bargaining while being firmly grounded in the collective model’s theory and identification strategy. Several extensions have followed including a useful simplification of this method allowing estimations on cross-sectional data (Lewbel and Pendakur, 2008), the extension of the latter to account explicitly for children (Bargain and Donni, 2012) or applications to specific groups like elderly couples (Cherchye et al., 2012). These analyses focus on rich countries. Very few applications have been carried out for developing countries, where it is suspected that intrahousehold inequality is the highest (using anthropometric evidence for the Philippines, Haddad and Kanbur, 1990, show for instance that a third of inter-individual inequality is explained by intrahousehold inequality). To the best of our knowledge, there are two exceptions. One is the extension of Bargain and Donni (2012) to multi-children households in Côte d’Ivoire (Bargain et al., 2014). The other is an estimation on data from Malawi that suggests a slightly different identification approach (Dunbar et al., 2013). Against this background, it seems there is a need to apply more widely this type of estimations for developing countries in order to embrace a broad range of possible results, assess potential regularities or explain differences across cultural and institutional settings. Such applications should also go beyond the mere calculation of sharing rules and be used to re-estimate poverty rates at the individual level in regions where within-household inequality may be present. Indeed, unequal allocations of resources can lead to the disadvantage of vulnerable household members, for instance women and children, while poverty is almost always assessed at the household level. This framework could also be used to test gender inequality within families (in particular in an African context, aforementioned studies provide some evidence of a pro-boy discrimination in Malawi but no boy-girl difference in Côte d’Ivoire). This is the path we take in the present paper. We provide evidence on resource shares in nuclear African families of South Africa, examine potential gender imbalances and characterise the degree of individual poverty for specific household members. Specifically, we address the following questions: What factors determine the balance of power in African households? How are resources distributed in the household? Is there evidence of gender imbalance in the allocation of household resources among adults and among children? What are the implications of household resource allocation decisions on individual poverty? How do economies of scale from living with others affect poverty among adults? While the present study does not make technical innovations, its contribution is at least twofold. First, as motivated above, it consolidates the literature by adding novel estimates to the very scarce literature on collective model estimations for relatively poor regions of the world. Notably, it questions the degree of intrahousehold and gender inequality in a different African context compared to existing evidence. Indeed, results for Malawi and Côte d’Ivoire, as cited above, cannot be generalised as they show somewhat relatively contrasting results, perhaps owing to peculiarities in socio-economic/political and cultural environments of these countries. It is therefore interesting to provide a comparison with the poor population of South Africa (Africans). Second, general empirical studies on intrahousehold relations in Africa are still limited. Previous studies on South Africa have typically focused on testing the unitary model. Kreuser (2013), Duflo (2000), Case (2002) and Wittenberg (2009) notably reject necessary conditions of the model. The proposed research goes beyond these studies by providing explicit information on the resource shares of household members. Recovering the sharing rule sheds light on whether household resource allocation decisions are laced with gender inequality due to power imbalances and whether conventional poverty measures based on household resources mask higher deprivation among certain populations. The rest of the paper is organised as follows. In Section 2 we present a brief background to the study, Section 3 presents the theoretical framework, the empirical model and the data. Section 4 discusses the estimation results and Section 5 provides a detailed poverty analysis and additional results. Section 6 concludes. 2. Background The Republic of South Africa is classified by the World Bank as an upper middle income country—its GDP per capita was US$6,600 in 2013 (ranked 89th)—but its Human Development Index lags behind (ranked 116th, cf. UNDP, 2015). The nation has about 52 million inhabitants classified as Whites (8.9%), Indians (2.5%), Coloreds (8.9%) and Africans (79.2%) (Statistics South Africa, 2012). These populations incur vast inequalities in wellbeing as sparked by separationist policies of the apartheid era (1948–1993). Twenty-three years post-apartheid, and despite a decrease in inter-racial inequality, access to quality education, economic opportunities, basic services, income and wealth is still skewed in favour of Whites followed by Indians, Coloreds and Africans. Hence, focusing on the latter group means we concentrate on the poorest segment of the South African population. Two aspects are of particular importance to motivate this point. First, inequality still persists in the country—the Gini coefficient increased from 0.57 in 1995 to 0.69 in 2011 (Hoogeveen and Ozler, 2005; Statistics South Africa, 2014)—but this trend seems to be exacerbated by an increase in within rather than between group inequalities, especially among Africans (Leibbrandt et al., 2012). Second, since the country’s distribution of household income still follows the inherited pattern, Africans predominate in low percentiles of the country’s income distribution. Poverty is evaluated at 45.5% of the South African population in 2011 (Leibbrandt et al., 2010; Statistics South Africa, 2014) and is mainly due to Africans. This figure is relatively comparable to that of Côte d’Ivoire or Malawi (see Dunbar et al., 2013; Bargain et al., 2014), which makes the comparison with these countries interesting. While the distribution of South African resources between households is well-known, the same does not apply to that within households and, consequently, to the poverty at individual levels. Currently, few research efforts have been made towards highlighting that African households do not operate as per the unitary model (Wittenberg, 2009). The small but growing consensus in the literature is that the allocation of expenditure in African households is sensitive to the income recipient’s identity, which refutes the altruism that is inherent in the unitary model (Duflo, 2003; Wittenberg, 2009). Although this hints at a certain degree of conflict in the household allocation process, the latter cannot be read from present studies. Regardless of the literature gap, factors that translate into individual bargaining power in two-adult African households seem to be somewhat tilted in favour of men. For instance, in 2014, 72.7% of women and 75.7% of men in South Africa had attained at least some secondary education (UNDP, 2015). However, that many women are educated suggests that they are more likely to bargain for more resources towards their children’s upkeep (Duflo, 2003). Moreover, relatively fewer women than men participate in the labour market—44.5% versus 60.5% in 2013. Women are also more prone to unemployment than men, e.g., in 2013, the official unemployment rates were 26.7% and 23.1%, respectively (Statistics South Africa, 2014). They also tend to work more often in the household or in survivalist occupations in the informal sector. Their median wages are less than men’s (Casale and Posel, 2002; Bhorat and Goga, 2013). Also, it may be that married African women’s bargaining power is further compromised by the cultural practice of having their husbands pay ‘lobola’ (bride-wealth) to their families so as to legitimise the union. Evidence is mixed on this point. Some individuals uphold this culture and opine that being lobola’d is a sign of respect and commitment that the husband will indeed take care of the wife.1 On the other hand, some equate being lobola’d to women being ‘bought by their husbands’ which reduces gender equity and women’s bargaining power within the households (Mwamwenda and Monyooe, 1997; Shope, 2006). Evidence pertaining to resource allocation among children, i.e., boys and girls in African households, is currently scant. For instance, Duflo (2000) shows that girls’ nutrition responds more than boys’ to pension income received by grandmothers. This study is, however, restricted to a single measure of needs. 3. Model and data 3.1 Overview and main assumptions Empirical evidence on intrahousehold allocation of resources has been mainly hampered by two well-known problems. First, surveys often report expenditure and consumption data aggregated at household level. As a result, individual shares of household resources are rarely observed. Second, there is joint consumption of some household goods and services (e.g., dwelling costs), making it difficult to allocate such consumption to a given individual. To address these problems, we estimate the intrahousehold allocation of resources (sharing rule) using a multi-person collective model with parental bargaining and economies of scale. We follow the approach developed by Bargain and Donni (2012) and recently applied by Bargain et al. (2014) to multi-children households in an African context. The identification of the model is inspired by the method designed by Rothbarth (1943) and Gronau (1988, 1991) and relies on the existence of exclusive goods (consumed only by certain types of individuals in the household, e.g., adult goods). The Rothbarth-Gronau method suggests retrieving household resource allocation between parents and children by examining the extent to which the presence of children depresses the household consumption of adult-specific goods.2 With this method, the direct utility or disutility from having children is necessarily assumed to be separable from consumption goods and ignored. Bargain and Donni (2012) have generalised the idea by using the fact that men and women consume assignable goods (e.g., male and female clothing). The approach starts with the assumption that the preferences of male and female adults in couples, regarding such assignable goods, can be inferred from the observation of expenditure on the same goods by similar adults living alone. This consists of two underlying assumptions: first it requires that preferences over exclusive goods are stable across marital/family statuses—this implies in particular some form of separability in the utility function, as stated above—and that there is no selection into marriage regarding consumption preferences. Another aspect of the generalisation pertains to the fact that the Rothbarth-Gronau approach does not take into account the existence of scale economies due to the publicness of some goods (the degree to which they are jointly consumed). Following the suggestion of Lewbel and Pendakur (2008), an ‘independent of base’ (IB) assumption implies that a function, independent of total expenditure, can characterise the way consumption of each individual in the household is scaled to represent economies from joint consumption. Note that the intrahousehold allocation process is explicitly grounded in the collective model framework, allowing for possibly diverging opinions of the parents. 3.2 Collective model of household consumption We now present an abridged version of the collective model used in Bargain et al. (2014). The model assumes three types of households indexed by n = 1 for single adults, n = 2 for childless couples and n = 3 for couples with children. Let superscript k = 1, ..., K index goods over which households make consumption decisions. Individuals are denoted by subscript i = 1 for men, i = 2 for women and i = 3 for children. The log household expenditure is denoted by x. Every household is characterised by a set of utility functions, one for each adult individual and one for the group of children (children are ‘unitary’). In single-person households (n = 1), individual log resources simply coincide with household log expenditure x. Multi-person households (n > 1) are additionally characterised by a set of scaling functions si,n(p,z) for i = 1, 2, which capture the cost savings experienced by person i as a result of scale economies in the household, and by a sharing function ηi,n(p,z), which defines the amount of resources accruing to each member i = 1, 2, 3. Both are functions of pandz, i.e., the vectors of prices and socio-demographic characteristics (e.g., age, education, region of residence, house ownership and employment status). For multi-person households, the decision making process inherent in the model occurs in two stages. In the first stage, household resources exp(x) are distributed to members according to the sharing rule: individual i living in household n>1 receives a resource share ηi,n of total expenditure exp(x). In the second stage, expenditures on all goods are chosen as if each individual solved her/his own utility maximisation problem subject to an individual budget constraint. Recall that as in the Rothbarth-Gronau approach, the stability of individual preferences across household types is the key hypothesis behind identification results (Bargain and Donni, 2012).3 Precisely, it is assumed that after controlling for joint consumption and resource sharing, an adult’s utility function is independent of household type n. From this, differences in expenditure patterns between a person living alone and a person living with others can be attributed to scaling and sharing functions only. More technical assumptions are also made for the complete identification of these two structural components. First, it is assumed that the sharing function does not depend on household total expenditure (cf., Lewbel and Pendakur, 2008; Bargain and Donni, 2012; Dunbar et al., 2013). This assumption is tested and supported by recent evidence (Menon et al., 2012; Bargain et al., 2014). Also, it is possibly allayed by including measures of household wealth other than total expenditure in individual shares. Second, it is assumed that the scaling function for scale economies is also independent from the total expenditure—and, hence, of the utility level—at which it is evaluated (the IB assumption). It results from these two assumptions that a pertinent welfare metric, the indifference scale, can be derived as Ii,n(p,z)=ηi,n(p,z)/si,n(p,z) and is itself independent from the level of utility (Lewbel and Pendakur, 2008; Bargain and Donni, 2012), i.e., a property traditionally imposed in the literature on equivalence scales. Indifference scales are nonetheless different from the latter as they compare the same individual in two situations (Lewbel, 2003). Indeed they represent the income adjustment applied to a person i living in a multi-person household for him/her to reach the same indifference curve as when living alone. The basic budget share of individual i for good k is denoted by wik, i.e., this would be the share spent on that good if he/she lived alone. Bargain and Donni (2012) show that the budget share equation of individual i for good k in household n is written with the following structure: ωi,nk(x,p,z)=λi,nk(p,z)+wik(p,x+logηi,n(p,z)−logsi,n(p,z),zi)where the basic budget share is scaled by λi,nk(p,z)=∂logsi,n(p,z)/∂pk, a price elasticity of the scale economies factor, and depends on the log of the individual expenditure rescaled by this factor. Household expenditure on each good k, denoted by Wnk, is the sum of individual expenditures on good k and, hence, is expressed as: Wnk(p,x,z)=∑i=1nηi,n(p,z)⋅[λi,nk(p,z)+wik(p,x+logηi,n(p,z)−logsi,n(p,z),zi)]. The measure of economies of scale si,n(p,z) is individual-specific since economies of scale may differ between individuals within the same household, depending on how they value the good which is jointly consumed.4 Note that the scaling factor ranges between ηi,n(p,z) for purely public consumption and 1 for purely private consumption. For children, a normalisation is required since they always live within the same family structure, i.e., λ3,3k(p,z)=0 and s3,3(p,z)=1 for k=1,...,K. Note also that taking their preferences as ‘unitary’ does not mean that we impose equal sharing among them: the total share of children may possibly depend on characteristics that include the number of boys versus girls, or the age of children, in order to check for potential discrimination. In a constant price regime, the price vector p is the same for all and can be taken out of the expressions above. Hence, this approach can be readily used on cross-sectional data, as initially suggested by Lewbel and Pendakur (2008). The detailed presentation of the model identification in the presence of children can be found in Bargain and Donni (2012) (see Lewbel and Pendakur, 2008, for childless couples, with slightly different assumptions). The demonstration starts with the identification of the basic budget share functions wik from a sample of single men and single women, given the assumption that preferences are stable across household types n. Then the sharing functions and scaling functions can be generically identified from the sample of couples, using expenditure on goods specifically consumed by adult males and females respectively. Since the basic budget share equations of children are unknown, the adding-up condition of sharing functions, i.e., ∑iηi,n(z)=1, is necessary to recover the children’s share.5 3.3 Specification The empirical specification of the model starts with basic budget share equations, for which we assume the following quadratic form:6 wi,n,jk=aik+bikzi,j+cik·(xi,n,j−eizi,j)+dik·(xi,n,j−eizi,j)2 fori=1,2,3andk=1,..,K,where j indexes sampled households and xi,n,j=xj+logηi,n,j−logsi,n,j denotes log resources for individual i living in household j of type n. For adult men and women (i = 1, 2), the parameters aik,bik,cik,dik,ei to be estimated are gender-specific but independent of household type n and the number of children, since basic budget share functions are assumed to be the same for single women (men) and for women (men) living in a couple. Note also that socio-demographic variables zi,j enter the specification through the translation of budget share equations (coefficient vector bik) and through the translation of log resources (coefficient vector ei). For adults, age and education enter into eizi,j, while the same variables plus women’s employment status, dummies for house ownership and urban residency enter into bikzi,j. In the case of children, the characteristics entering bikzi,j include the number of children, their average age and the proportion of boys. Household budget share equations are specified as follows. For single men and women, these coincide with the budget share equations wik plus an additive error term: W1,jk=wik(x,zi,j)+ε1,jk. For multi-person households and for non-adult-specific goods, the household budget share equations Wn,jk=∑i=1nηi,n,j[λi,n,jk+wik(xj+logηi,n,j−logsi,n,j,zi,j)]+εn,jk forn>1comprise the basic budget functions as already specified and three other components. First, the sharing functions ηi,n,j defined by the logistic form: ηi,n,j=exp(αiη+βiηzi,jη)∑ι=1nexp(αιη+βιηzι,jη),fori=1,2,3.where zi,jη are characteristics that include, for adults, age, education, urban residency, house ownership and women’s employment status, and for children, mother’s education and employment status, urban residence, average age of children, proportion of male children and number of children in the household. Second, the log scaling functions that translate expenditure in the basic budget shares are specified as: si,n,j=ηi,n,jσi,n,j+ηi,n,j−σi,n,jηi,n,j,with σi,n,j=γi+δizi,hσfor i=1,2where the normalised scale σi,n,j ranges from 0 (purely private consumption) to 1 (purely public). The normalised scale takes a linear form with parameters γi and δi, zi,hσ only including number of children. Note that with the different estimates presented hereafter, the scales are effectively in the range [0,1] without imposing such restriction in the estimation process. Third, the price elasticity that translates the basic budget shares λi,nk(z) poses the usual challenge of measuring price effects and is therefore restricted to be constant (normalised to zero for children): λi,nk(z)=λ¯i,nk,fori=1,2,3,n=2,3,and k=1,…,K. The model is estimated by the iterated SURE method. To account for potential correlation between the error terms εn,jk and the log total expenditure, each budget share equation is augmented with the ‘Wu-Hausman’ residuals obtained from reduced-form estimations of x on all exogenous variables used in the model plus some excluded instruments, namely a third order polynomial in household disposable income (cf. Blundell and Robin, 1999). The error terms are supposed to be uncorrelated across households but correlated across goods within households and homoscedastic within each family type. 3.4 Data and selection We use data drawn from the 2010/11 South African Income and Expenditure Survey (IES) conducted by Statistics South Africa. This is a nationally representative cross-sectional dataset with detailed information on household consumption, demographics and economic activities. The initial sample consists of 25,328 households. As motivated above, the sample is restricted to African households thereby eliminating about 21% of the initial sample. African households represent the country’s majority and were the most disadvantaged group in apartheid South Africa. This restriction allows us to focus on a more homogeneous group with a reasonable sample size. In addition, it facilitates comparison of our results with those for poor population from other African countries (in particular aforementioned studies on Côte d’Ivoire and Malawi). The sample is further restricted to monogamous, nuclear households, which drops a further 38%. The extension beyond nuclear households, i.e., to other members or the extended family, is a daunting challenge for structural models and their identification (a rare example can be found in Donni and El Badaoui, 2014, for a three-generation model of labour supply with application to South Africa). We also drop couples with children aged above 14 or with more than three children (5%),7 single mothers and single fathers (8%), and households with missing information on education or with heads aged below 20 or above 65 (4%). Finally, we discard households with ‘inconsistent’8 reports on clothing, zero food expenditures and outliers (7%). This sample delimitation process leaves a final sample of 4,212 households (17% of the initial sample and 21% of the African households), composed of single men, single women and couples with 0–3 children. Tables 1 and 2 present descriptive statistics on household characteristics and expenditure for our selected sample. Table 1: Descriptive Statistics on Household Characteristics Single Men Single Women Childless Couple Couple + 1 child Couple + 2 children Couple + 3 children Average child age – – – – – – 4.9 (4.46) 7.6 (3.97) 9.0 (3.35) Prop. of male children – – – – – – 0.498 (0.501) 0.500 (0.374) 0.492 (0.303) House ownership 0.467 (0.499) 0.397 (0.490) 0.486 (0.500) 0.495 (0.501) 0.623 (0.485) 0.715 (0.452) Number of rooms 1.490 (1.916) 1.493 (2.134) 1.989 (2.399) 2.053 (2.353) 2.641 (2.423) 3.331 (2.490) Urban 0.571 (0.495) 0.605 (0.489) 0.610 (0.488) 0.677 (0.468) 0.616 (0.487) 0.536 (0.500) Men Age 37.4 (11.49) – – 40.7 (11.473) 37.2 (8.994) 39.7 (8.153) 41.5 (7.110) Low education 0.275 (0.447) – – 0.317 (0.466) 0.173 (0.378) 0.252 (0.434) 0.275 (0.447) Employed 0.821 (0.384) 0.786 (0.410) 0.868 (0.339) 0.834 (0.372) 0.847 (0.360) Women Age – – 40.1 (13.02) 36.6 (11.13) 31.7 (8.06) 34.7 (7.26) 36.1 (6.02) Low education – – 0.276 (0.448) 0.296 (0.457) 0.157 (0.364) 0.215 (0.411) 0.224 (0.417) Employed – – 0.724 (0.448) 0.499 (0.500) 0.343 (0.475) 0.435 (0.496) 0.390 (0.489) Number of households 1663 572 706 440 536 295 Single Men Single Women Childless Couple Couple + 1 child Couple + 2 children Couple + 3 children Average child age – – – – – – 4.9 (4.46) 7.6 (3.97) 9.0 (3.35) Prop. of male children – – – – – – 0.498 (0.501) 0.500 (0.374) 0.492 (0.303) House ownership 0.467 (0.499) 0.397 (0.490) 0.486 (0.500) 0.495 (0.501) 0.623 (0.485) 0.715 (0.452) Number of rooms 1.490 (1.916) 1.493 (2.134) 1.989 (2.399) 2.053 (2.353) 2.641 (2.423) 3.331 (2.490) Urban 0.571 (0.495) 0.605 (0.489) 0.610 (0.488) 0.677 (0.468) 0.616 (0.487) 0.536 (0.500) Men Age 37.4 (11.49) – – 40.7 (11.473) 37.2 (8.994) 39.7 (8.153) 41.5 (7.110) Low education 0.275 (0.447) – – 0.317 (0.466) 0.173 (0.378) 0.252 (0.434) 0.275 (0.447) Employed 0.821 (0.384) 0.786 (0.410) 0.868 (0.339) 0.834 (0.372) 0.847 (0.360) Women Age – – 40.1 (13.02) 36.6 (11.13) 31.7 (8.06) 34.7 (7.26) 36.1 (6.02) Low education – – 0.276 (0.448) 0.296 (0.457) 0.157 (0.364) 0.215 (0.411) 0.224 (0.417) Employed – – 0.724 (0.448) 0.499 (0.500) 0.343 (0.475) 0.435 (0.496) 0.390 (0.489) Number of households 1663 572 706 440 536 295 Notes: Standard deviation in parentheses. Low education is composed of people with no schooling or primary education. Table 2: Descriptive Statistics on Household Expenditure Single Men Single Women Childless Couple Couple + 1 child Couple + 2 children Couple + 3 children Budget shares Food 0.291 (0.152) 0.291 (0.140) 0.293 (0.147) 0.305 (0.127) 0.315 (0.138) 0.331 (0.141) Alcohol 0.054 (0.089) 0.009 (0.033) 0.040 (0.073) 0.017 (0.041) 0.019 (0.040) 0.016 (0.041) Women’s clothing – 0.060 (0.053) 0.041 (0.040) 0.035 (0.032) 0.026 (0.029) 0.022 (0.026) Men’s clothing 0.073 (0.070) – – 0.046 (0.052) 0.037 (0.039) 0.030 (0.034) 0.027 (0.037) Children’s clothing – – – – – – 0.029 (0.025) 0.041 (0.035) 0.045 (0.038) Housing 0.228 (0.138) 0.257 (0.134) 0.223 (0.134) 0.219 (0.125) 0.209 (0.136) 0.199 (0.127) Transport and comm. 0.175 (0.126) 0.183 (0.120) 0.176 (0.115) 0.163 (0.097) 0.162 (0.104) 0.158 (0.099) Household utilities 0.080 (0.086) 0.093 (0.106) 0.096 (0.095) 0.095 (0.079) 0.106 (0.084) 0.111 (0.092) Leisure goods and serv. 0.075 (0.094) 0.066 (0.091) 0.052 (0.065) 0.056 (0.065) 0.051 (0.064) 0.053 (0.064) Personal goods and serv. 0.024 (0.034) 0.042 (0.047) 0.031 (0.039) 0.045 (0.050) 0.041 (0.046) 0.038 (0.040) Prop. of zero purchases on Women’s clothing – – 0.086 (0.280) 0.147 (0.355) 0.095 (0.294) 0.166 (0.372) 0.180 (0.385) Men’s clothing 0.127 (0.334) – – 0.197 (0.398) 0.175 (0.380) 0.239 (0.427) 0.231 (0.422) Children’s clothing – – – – – 0.082 (0.274) 0.090 (0.286) 0.051 (0.220) Household expenditure1 In Rand/month 1951.50 (1686.21) 2035.71 (1583.88) 2838.68 (2675.09) 3284.15 (2817.18) 3670.51 (3286.55) 3990.07 (3807.17) In USD/month 266.96 (230.67) 278.48 (216.67) 388.33 (365.95) 449.27 (385.39) 502.12 (449.60) 545.84 (520.82) Prop. of hh exp used 0.722 0.705 0.670 0.683 0.648 0.677 Single Men Single Women Childless Couple Couple + 1 child Couple + 2 children Couple + 3 children Budget shares Food 0.291 (0.152) 0.291 (0.140) 0.293 (0.147) 0.305 (0.127) 0.315 (0.138) 0.331 (0.141) Alcohol 0.054 (0.089) 0.009 (0.033) 0.040 (0.073) 0.017 (0.041) 0.019 (0.040) 0.016 (0.041) Women’s clothing – 0.060 (0.053) 0.041 (0.040) 0.035 (0.032) 0.026 (0.029) 0.022 (0.026) Men’s clothing 0.073 (0.070) – – 0.046 (0.052) 0.037 (0.039) 0.030 (0.034) 0.027 (0.037) Children’s clothing – – – – – – 0.029 (0.025) 0.041 (0.035) 0.045 (0.038) Housing 0.228 (0.138) 0.257 (0.134) 0.223 (0.134) 0.219 (0.125) 0.209 (0.136) 0.199 (0.127) Transport and comm. 0.175 (0.126) 0.183 (0.120) 0.176 (0.115) 0.163 (0.097) 0.162 (0.104) 0.158 (0.099) Household utilities 0.080 (0.086) 0.093 (0.106) 0.096 (0.095) 0.095 (0.079) 0.106 (0.084) 0.111 (0.092) Leisure goods and serv. 0.075 (0.094) 0.066 (0.091) 0.052 (0.065) 0.056 (0.065) 0.051 (0.064) 0.053 (0.064) Personal goods and serv. 0.024 (0.034) 0.042 (0.047) 0.031 (0.039) 0.045 (0.050) 0.041 (0.046) 0.038 (0.040) Prop. of zero purchases on Women’s clothing – – 0.086 (0.280) 0.147 (0.355) 0.095 (0.294) 0.166 (0.372) 0.180 (0.385) Men’s clothing 0.127 (0.334) – – 0.197 (0.398) 0.175 (0.380) 0.239 (0.427) 0.231 (0.422) Children’s clothing – – – – – 0.082 (0.274) 0.090 (0.286) 0.051 (0.220) Household expenditure1 In Rand/month 1951.50 (1686.21) 2035.71 (1583.88) 2838.68 (2675.09) 3284.15 (2817.18) 3670.51 (3286.55) 3990.07 (3807.17) In USD/month 266.96 (230.67) 278.48 (216.67) 388.33 (365.95) 449.27 (385.39) 502.12 (449.60) 545.84 (520.82) Prop. of hh exp used 0.722 0.705 0.670 0.683 0.648 0.677 Notes: Standard deviation in parentheses. 1We indicate the level of household expenditure considered in the structural model (in Rand and in USD, using the 2010 exchange rate of $1 = R7.31). Some expenditure is not included (e.g., education, health), so we indicate the proportion that it represents in percentage of total household expenditure. The main message from Table 1 is that adults are not very different across household type, which is a reassuring observation regarding our identifying assumption. This is true regarding the proportion of urban households, adult men and women’s age and education level, as well as employment rates for men. Labour market participation of single women is much larger, as could be expected. Among couples with children, child characteristics are also fairly comparable, with a similar proportion of boys. The age of children as well as the household ownership rate and the dwelling size logically increase with family size. Strictly, the model only requires the existence of gender-assignable adult goods (e.g., male and female clothing, see for instance Deaton, 1989) and a residual good in order to identify the resource shares of men, women and children. However, to improve efficiency, we also consider other non-durable goods in the estimations, namely, food, housing, transport and communication, household utilities, leisure goods and services (which is combined with alcohol expenditure), and personal goods and services, as well as a child-specific good (i.e., child clothing). As a result, Table 2 reports household budget shares by household type for these various goods. Expenditure on services such as education, health care, insurance and durable goods (e.g., cars and furniture) were excluded as they might represent selected, possibly occasional expenditure.9 We shall present a baseline in which expenditures on housing are not modelled—this is a conventional choice pertaining to the fact that housing costs are difficult to measure for owners and those living in rural areas. Nonetheless, expenditure on housing may be an important contributor to household economies of scale, so we include it in a variant of the main model (housing costs were imputed using regressions on a variety of dwelling characteristics). In the upper part of Table 2, we see that households allocate about a third of their resources to food, which indicates that these households are relatively poor. We also notice that the budget share of the typically private goods (notably the total expenditure on male, female and child clothing) increases with the size of the household while the budget share of typically public goods (i.e., housing and to a less extent transport) decreases. This reflects to some extent the fact that economies of scale are substantial but are not the same for all goods. The increase in food share is mainly due to children (children are more food intensive than parents, a well-known argument against the Engel approach—and in favour of the Rothbarth approach—to measure child cost). Importantly, the presence of children in the household reduces the budget shares devoted to parents’ clothing. This pattern is consistent with the intuition of the Rothbarth-Gronau approach and the identification of child resources suggested in this paper and in previous studies of that type. That is, the arrival of a child implies a negative income effect on parents’ consumption, corresponding to the resources re-allocated to the child. Comparing couples with one, two and three children, we also remark that female clothing decreases more rapidly than male’s as the family grows, which denotes a higher sacrifice by mothers to accommodate their children and possibly a lower overall resource share of women in larger household (of course, this may also reflect endogenous selection in terms of fertility, which we cannot address easily in the present framework). The fact that men’s clothing expenditure declines more rapidly than women’s in couples with none or one child might just indicate that men benefit from higher economies of scale than women due to these transitions. Finally, Table 2 shows an encouragingly low proportion of zero values for male and female adult clothing (the identifying goods) and child clothing. The last rows report total expenditure, which expectedly increases with household size, and the fraction of total expenditure used in our baseline demand system, which is relatively similar across household types. 4. Estimation results Our baseline model excludes housing expenditure and hence consists of a K – 1 = 7 good system with household utilities as the residual good. This system then comprises 4 non-exclusive goods, with three individual budget shares (two for the adults and one for children), and 3 assignable goods (adult male, adult female and child clothing), hence a total of 15 individual Engel curves. In this system we estimate 180 parameters, of which 47% are statistically different from zero at 5% and 10% levels. Table 3 first presents estimates of resource shares, scaling factors and indifference scales for this baseline model I. Variants are also presented that restrict parameters in the scaling function to be identical for men and women (model II) and that include housing expenditure in the budget share system (model III)—for sensitivity tests on estimated economies of scale. Standard errors of these models presented in parentheses are heteroscedastic consistent. In our discussion, we first consider resource shares, followed by economies of scale and indifference scales, respectively.10 Table 3: Household Resource Shares, Scaling Factors and Indifference scales Model I Model II Model III Baseline Model Model with Identical σi,n Model with Housing Coef. Std.err Coef. Std.err Coef. Std.err Panel A: Resource Shares Couple with no children Women 0.447 (0.067) 0.425 (0.066) 0.454 (0.045) Men 0.553 (0.067) 0.575 (0.066) 0.546 (0.045) Couple with 1 child Women 0.360 (0.064) 0.347 (0.062) 0.358 (0.048) Men 0.446 (0.072) 0.469 (0.072) 0.430 (0.044) Children 0.195 (0.083) 0.184 (0.079) 0.212 (0.060) Couple with 2 children Women 0.325 (0.068) 0.316 (0.066) 0.342 (0.048) Men 0.403 (0.080) 0.427 (0.079) 0.410 (0.047) Children 0.272 (0.111) 0.257 (0.106) 0.248 (0.067) Couple with 3 children Women 0.283 (0.075) 0.278 (0.071) 0.323 (0.050) Men 0.350 (0.090) 0.375 (0.090) 0.388 (0.053) Children 0.367 (0.141) 0.347 (0.136) 0.289 (0.081) Panel B: Scaling Factors Couple with no children Women 0.876 (0.232) 0.766 (0.252) 0.821 (0.162) Men 0.759 (0.185) 0.857 (0.147) 0.706 (0.106) Couple with 1 child Women 0.817 (0.275) 0.689 (0.267) 0.704 (0.183) Men 0.664 (0.215) 0.786 (0.181) 0.577 (0.114) Couple with 2 children Women 0.777 (0.287) 0.645 (0.261) 0.642 (0.172) Men 0.617 (0.218) 0.746 (0.187) 0.534 (0.106) Couple with 3 children Women 0.725 (0.317) 0.589 (0.264) 0.582 (0.164) Men 0.556 (0.225) 0.692 (0.206) 0.490 (0.100) Panel C: Indifference Scale Couple with no children Women 0.510 (0.130) 0.555 (0.153) 0.553 (0.106) Men 0.729 (0.204) 0.671 (0.150) 0.773 (0.141) Couple with 1 child Women 0.440 (0.137) 0.503 (0.157) 0.509 (0.129) Men 0.671 (0.228) 0.596 (0.160) 0.746 (0.166) Couple with 2 children Women 0.418 (0.145) 0.489 (0.156) 0.532 (0.140) Men 0.652 (0.230) 0.572 (0.161) 0.769 (0.169) Couple with 3 children Women 0.390 (0.163) 0.471 (0.165) 0.555 (0.156) Men 0.630 (0.236) 0.543 (0.170) 0.793 (0.176) Model I Model II Model III Baseline Model Model with Identical σi,n Model with Housing Coef. Std.err Coef. Std.err Coef. Std.err Panel A: Resource Shares Couple with no children Women 0.447 (0.067) 0.425 (0.066) 0.454 (0.045) Men 0.553 (0.067) 0.575 (0.066) 0.546 (0.045) Couple with 1 child Women 0.360 (0.064) 0.347 (0.062) 0.358 (0.048) Men 0.446 (0.072) 0.469 (0.072) 0.430 (0.044) Children 0.195 (0.083) 0.184 (0.079) 0.212 (0.060) Couple with 2 children Women 0.325 (0.068) 0.316 (0.066) 0.342 (0.048) Men 0.403 (0.080) 0.427 (0.079) 0.410 (0.047) Children 0.272 (0.111) 0.257 (0.106) 0.248 (0.067) Couple with 3 children Women 0.283 (0.075) 0.278 (0.071) 0.323 (0.050) Men 0.350 (0.090) 0.375 (0.090) 0.388 (0.053) Children 0.367 (0.141) 0.347 (0.136) 0.289 (0.081) Panel B: Scaling Factors Couple with no children Women 0.876 (0.232) 0.766 (0.252) 0.821 (0.162) Men 0.759 (0.185) 0.857 (0.147) 0.706 (0.106) Couple with 1 child Women 0.817 (0.275) 0.689 (0.267) 0.704 (0.183) Men 0.664 (0.215) 0.786 (0.181) 0.577 (0.114) Couple with 2 children Women 0.777 (0.287) 0.645 (0.261) 0.642 (0.172) Men 0.617 (0.218) 0.746 (0.187) 0.534 (0.106) Couple with 3 children Women 0.725 (0.317) 0.589 (0.264) 0.582 (0.164) Men 0.556 (0.225) 0.692 (0.206) 0.490 (0.100) Panel C: Indifference Scale Couple with no children Women 0.510 (0.130) 0.555 (0.153) 0.553 (0.106) Men 0.729 (0.204) 0.671 (0.150) 0.773 (0.141) Couple with 1 child Women 0.440 (0.137) 0.503 (0.157) 0.509 (0.129) Men 0.671 (0.228) 0.596 (0.160) 0.746 (0.166) Couple with 2 children Women 0.418 (0.145) 0.489 (0.156) 0.532 (0.140) Men 0.652 (0.230) 0.572 (0.161) 0.769 (0.169) Couple with 3 children Women 0.390 (0.163) 0.471 (0.165) 0.555 (0.156) Men 0.630 (0.236) 0.543 (0.170) 0.793 (0.176) Note: Standard errors are heteroscedastic consistent. 4.1 Resource shares We compute resource shares ηi,n for all the individuals in the sample and present the average by type of individual (man, woman, children) and type of household. Results are reported in panel A of Table 3. Model I corresponds to our baseline model estimated with the sample described in the previous section. The scaling function is restricted to be gender invariant in model II while housing is added to the demand system in model III. We observe that the share of total household resources accruing to the wife is lower than that of the husband. This result is relatively stable across the three models,11 and is true in all demographic groups. Precisely, in childless couples, 44.7% of household resources are allocated to women and 55.3% to their husbands. In couples with children, the ratio of the women’s share over the total adult share is very similar, i.e., around 45% with models I and II and 43% with model II, and does not vary with the number of children. Note that the difference between female and male shares is not statistically significant, which is obviously due to the imprecise estimates derived from estimations on small samples (this is also the case in Bargain et al., 2014).12 For children, the model can only identify their total resource share, not individual shares. The estimated resource share for a single child is close to the measured cost of children in richer countries (see Bargain and Donni, 2012, for a discussion), i.e., he/she receives about 19.5% of the household resources in the baseline and between 18.4% and 21.2% across models. Naturally, children’s resource shares increase with family size. Yet the per-child resource tends to decrease quite drastically, as found in other studies (Dunbar et al., 2013; Bargain et al., 2014). It is between 12.4 and 13.6% in couples with two children and 9.6–12.2% in couples with three. Note that the resource share estimates are again fairly stable across models. If sharing was conducted according to needs, our results would be interpreted as follows: a child represents between 54 and 59% (across models) of the need of the mother in one-child couples, 36–42% in two-child couples and 30–43% in three-child couples. The child share represents 22.5–27% of the need of the couple in one-child family, 16.5–18.7% in two-child couples and 13.5–19% in three-child couples. This is in the range of what is supposed to be the need of a child in the modified OECD scale (20% of the need of the couple); for the first child, it is close to values suggested by Deaton (according to Woolard and Leibbrandt, 1999) and lower than estimates based on the Engel method using South African data (Woolard, 2002). 4.2 Economies of scale and indifference scales Panel B of Table 3 presents estimates for si,n, the scaling factor for adult economies of scale. These estimates are fairly imprecise but reveal interesting patterns nonetheless. Recall that for a couple without children, they must lie between the resource share (consumption is then viewed as purely public) and 1 (purely private). In all models, the fact that these scales are lower than 1, especially for men, underlines the possible existence of economies of scale in the household, which invalidates the traditional Rothbarth approach. For instance, a scale of 0.76 for a man without children in the baseline suggests that his cost of living in a couple is 76% of the cost he would experience if living alone. Consistently with the interpretation of these scaling factors, their size, and hence the degree of scale economies, increase with family size. Note that in model II, normalised scales σi,n are forced to be equal for men and women, but original scales si,n may still vary across spouses as they also depend on the resource shares. In model III, scales si,n are smaller than in the baseline, i.e., the publicness of adult consumption increases due to the fact that housing expenditure is taken into account. Panel C of Table 3 reports indifference scales Ii,n=ηi,n/si,n. As discussed earlier, they represent the welfare effect of living with others due to sharing and joint consumption, expressed as a fraction of household expenditure needed to attain the same welfare when living alone. Our baseline estimates show that, if a childless married woman were to live alone, she would require 51% of her couple’s budget to be as well off as when living with her partner. This figure increases when economies of scale in couples are large (i.e., si,n is small). It also increases with her resource share. Hence it is an interesting individual welfare measure that reflects the combined role of unequal distribution and joint consumption. In model II, identical σi,n for both spouses make indifference scales depend only on the sharing rule, which explains the smaller difference between men and women (since the resource shares are less contrasted than economies of scale). Indifference scales in model III reveal the high scale economies due to the inclusion of housing, and the welfare gain compared to the baseline is fairly similar in magnitude for men and women, in all family configurations. 4.3 Estimates of the sharing rule In Table 4, we report the parameter estimates of the sharing and scaling functions in order to better understand the household resource allocation process. With reference to the baseline model, results for the sharing function show that the share of expenditure allocated to a spouse increases with own age and education. These effects are statistically significant in two out of the three model specifications. In addition, a woman’s employment significantly increases her share of total resources in all three models. Home owners tend to be more equal as the male share declines significantly. To some extent, these findings also suggest that wealth proxies play a non-trivial role in the allocation of resources among couples. Table 4: Parameters of the Sharing Function Model I Model II Model III Baseline Model Model with Identical σi,n Model with Housing Coef. Std.err Coef. Std.err Coef. Std.err Women’s Share Constant – – – – – – Women’s age 0.015 (0.009) 0.017 (0.008) 0.015 (0.007) Women low education −0.315 (0.170) −0.343 (0.156) −0.236 (0.140) Urban – – – – – – Woman’s employment 0.246 (0.129) 0.261 (0.102) 0.300 (0.104) House owner – – – – – – Men’s Share Constant −0.849 (0.446) −0.873 (0.469) −0.529 (0.297) Men’s age 0.018 (0.009) 0.019 (0.008) 0.014 (0.007) Men low education −0.310 (0.169) −0.321 (0.149) −0.596 (0.127) House owner −0.237 (0.125) −0.242 (0.118) −0.201 (0.100) Urban −0.060 (0.161) −0.050 (0.140) −0.343 (0.117) Children’s Share Constant −2.011 (0.632) −2.062 (0.629) −1.558 (0.445) Number of children 0.437 (0.101) 0.428 (0.100) 0.206 (0.109) Prop. of male children 0.188 (0.133) 0.190 (0.132) 0.245 (0.180) Ave. age of children 0.099 (0.041) 0.103 (0.041) 0.065 (0.020) Urban 0.207 (0.133) 0.225 (0.129) 0.255 (0.175) Mother low education −0.208 (0.122) −0.221 (0.107) −0.190 (0.114) Mother employed 0.205 (0.099) 0.215 (0.085) 0.293 (0.097) Model I Model II Model III Baseline Model Model with Identical σi,n Model with Housing Coef. Std.err Coef. Std.err Coef. Std.err Women’s Share Constant – – – – – – Women’s age 0.015 (0.009) 0.017 (0.008) 0.015 (0.007) Women low education −0.315 (0.170) −0.343 (0.156) −0.236 (0.140) Urban – – – – – – Woman’s employment 0.246 (0.129) 0.261 (0.102) 0.300 (0.104) House owner – – – – – – Men’s Share Constant −0.849 (0.446) −0.873 (0.469) −0.529 (0.297) Men’s age 0.018 (0.009) 0.019 (0.008) 0.014 (0.007) Men low education −0.310 (0.169) −0.321 (0.149) −0.596 (0.127) House owner −0.237 (0.125) −0.242 (0.118) −0.201 (0.100) Urban −0.060 (0.161) −0.050 (0.140) −0.343 (0.117) Children’s Share Constant −2.011 (0.632) −2.062 (0.629) −1.558 (0.445) Number of children 0.437 (0.101) 0.428 (0.100) 0.206 (0.109) Prop. of male children 0.188 (0.133) 0.190 (0.132) 0.245 (0.180) Ave. age of children 0.099 (0.041) 0.103 (0.041) 0.065 (0.020) Urban 0.207 (0.133) 0.225 (0.129) 0.255 (0.175) Mother low education −0.208 (0.122) −0.221 (0.107) −0.190 (0.114) Mother employed 0.205 (0.099) 0.215 (0.085) 0.293 (0.097) Notes: Standard errors are heteroscedastic consistent. Estimated parameters and standard errors indicated by a dash are set to zero for identification purposes. The share of children is positively and strongly related to their number and their age, as expected. There is mild evidence that child shares are lower when the mother has lower education. They increase very significantly when mothers are employed, which may be consistent with the fact that mothers are more inclined to support their children and can do so more easily when they get their own earnings. This is also much in line with the substantial literature showing the effect of women’s empowerment on child nutrition and welfare (for instance Fafchamps et al., 2009). The results do not present evidence of a gender bias among children.13 Finally, there is no particular effect attached to urban households. It is notable that all these results are qualitatively similar across our different model specifications. Note that estimates of the individual budget share equations for adults and children are presented in Tables A.1 and A.2 of the Appendix, respectively. 5. Poverty analysis and additional results 5.1 Implications on poverty measurement We now address the distributional implications of our estimations. The first three columns of Table 5 examine the distribution of individual consumption for the different household members, focusing on the baseline model. It turns out that our parsimonious specification of the sharing rule already manages to create a large dispersion of resource shares across households. Precisely, the total expenditure share of a man (woman) living in a childless couple varies between 40% and 80% (20–60%) depending on the characteristics. The range is quite wide and is always lower for women across all types of households. In fact, in households with children, the range of male shares is always around 24–62% while the range of female shares decreases with the number of children, down to 14–40% for three children. For children, the distribution of total expenditure shares also shows significant variation. Table 5: Poverty Measurement Resource Shares (Baseline Model) Poverty Head Count Min. Med. Max. Per-capita Expenditure I (High Child Need) II (Low Child Need) III (‘Adjusted’ Adult Shares) Single men 1.000 1.000 1.000 0.036 (0.005) 0.036 (0.005) 0.036 (0.005) 0.036 (0.005) Single women 1.000 1.000 1.000 0.024 (0.006) 0.024 (0.006) 0.024 (0.006) 0.024 (0.006) Couples with no children Women 0.198 0.413 0.599 0.205 (0.015) 0.285 (0.017) 0.285 (0.017) 0.221 (0.016) Men 0.401 0.587 0.802 0.205 (0.015) 0.152 (0.014) 0.152 (0.014) 0.081 (0.010) Couples with 1 child Women 0.169 0.344 0.582 0.222 (0.021) 0.224 (0.021) 0.224 (0.021) 0.137 (0.017) Men 0.244 0.418 0.624 0.222 (0.021) 0.156 (0.018) 0.156 (0.018) 0.051 (0.011) Children 0.109 0.218 0.446 0.222 (0.021) 0.254 (0.022) 0.107 (0.015) Couples with 2 children Women 0.165 0.301 0.467 0.350 (0.021) 0.259 (0.019) 0.259 (0.019) 0.160 (0.016) Men 0.241 0.408 0.609 0.350 (0.021) 0.169 (0.016) 0.169 (0.016) 0.039 (0.008) Children 0.125 0.279 0.507 0.350 (0.021) 0.417 (0.021) 0.241 (0.019) Couples with 3 children Women 0.143 0.247 0.405 0.412 (0.030) 0.290 (0.028) 0.290 (0.028) 0.162 (0.022) Men 0.233 0.342 0.631 0.412 (0.030) 0.217 (0.025) 0.217 (0.025) 0.037 (0.011) Children 0.212 0.399 0.609 0.412 (0.030) 0.430 (0.030) 0.265 (0.027) Resource Shares (Baseline Model) Poverty Head Count Min. Med. Max. Per-capita Expenditure I (High Child Need) II (Low Child Need) III (‘Adjusted’ Adult Shares) Single men 1.000 1.000 1.000 0.036 (0.005) 0.036 (0.005) 0.036 (0.005) 0.036 (0.005) Single women 1.000 1.000 1.000 0.024 (0.006) 0.024 (0.006) 0.024 (0.006) 0.024 (0.006) Couples with no children Women 0.198 0.413 0.599 0.205 (0.015) 0.285 (0.017) 0.285 (0.017) 0.221 (0.016) Men 0.401 0.587 0.802 0.205 (0.015) 0.152 (0.014) 0.152 (0.014) 0.081 (0.010) Couples with 1 child Women 0.169 0.344 0.582 0.222 (0.021) 0.224 (0.021) 0.224 (0.021) 0.137 (0.017) Men 0.244 0.418 0.624 0.222 (0.021) 0.156 (0.018) 0.156 (0.018) 0.051 (0.011) Children 0.109 0.218 0.446 0.222 (0.021) 0.254 (0.022) 0.107 (0.015) Couples with 2 children Women 0.165 0.301 0.467 0.350 (0.021) 0.259 (0.019) 0.259 (0.019) 0.160 (0.016) Men 0.241 0.408 0.609 0.350 (0.021) 0.169 (0.016) 0.169 (0.016) 0.039 (0.008) Children 0.125 0.279 0.507 0.350 (0.021) 0.417 (0.021) 0.241 (0.019) Couples with 3 children Women 0.143 0.247 0.405 0.412 (0.030) 0.290 (0.028) 0.290 (0.028) 0.162 (0.022) Men 0.233 0.342 0.631 0.412 (0.030) 0.217 (0.025) 0.217 (0.025) 0.037 (0.011) Children 0.212 0.399 0.609 0.412 (0.030) 0.430 (0.030) 0.265 (0.027) Notes: Standard errors in parentheses. Compared to poverty rate based on per capita expenditure, columns I–III show rates of individual poverty under three scenarios. In column I, the child poverty line is set at 60% of adult requirements, in II it is set at 40% of adult requirements, in III adult resource shares are adjusted for economies of scale. The rest of Table 5 suggests an original poverty analysis based on individual expenditure. Using previous estimates, we examine whether resources allocated to each individual are sufficient to meet their minimum requirements for a decent standard of living. Estimated resource shares are used to calculate the actual resources accruing to each adult (unadjusted individual resources yi,n=exp[x+logηi,n(z)] for i = 1, 2, with ηi,n=1 for singles). Estimated scaling factors are additionally used to calculate adjusted resources (scale-weighted individual resources: ÿi,n=exp[x+logIi,n(z)]). For children, we simply divide the total child resources by the number of children in the household. These individualised level of expenditure are then compared to poverty lines defined as follows. We primarily use the 2010 monthly national poverty line of R594 (US$81.2) per adult and R356 (US$48.7) per child, as reported by Statistics South Africa (2014) and defined as the level of consumption below which individuals are unable to meet their minimum monthly food and non-food requirements.14 The minimum requirement for children applies a conservative ratio of 0.6 to an adult, which is in line with our earlier finding on a child’s share relative to the mother’s (‘high child need’). Inversely, we also calibrate a poverty line in order to make the overall level of child poverty similar to that of adults’, namely a child poverty line around 40% of adult requirements (‘low child need’). Finally, to examine the implications of ignoring intrahousehold sharing when measuring poverty, we also compare per-capita expenditure to a household poverty line calculated using the above thresholds for each individual composing the household. Results in Table 5 first show that poverty among single men and women is very low (4% and 2%), possibly due to the high employment rate in this group. The per capita poverty rate is 21% for couples without children. It increases with household size, especially for families with two (poverty rate of 35%) or three children (41%). We then move to poverty measures accounting for unequal resource allocation. We find that poverty is more prevalent among women than men, for instance a female poverty rate of 28% in childless couples versus 15% of men, and 29% versus 22% in large families. A close look shows that, barring women in childless couples, the per capita measure overestimates poverty rates for both sexes. When resource shares are adjusted for scaling factors, poverty rates decrease considerably, especially for men who benefit from larger economies of scale (a similar result is found for Côte d’Ivoire in Bargain et al., 2014). The poverty rates of married women are now found in a range of 16–22% across family types (instead of 22–29%) while those of married men fall as low as 4–8% (instead of 15–22%). At least for men, this pattern shows that, for all family types, poverty rates of adults living in a family are of the same order as those of single individuals. Ominously, we observe very high poverty rates among children, from 25% in one-child families to 43% for three-child families when using measure I (‘high child need’). In all family types, this is larger than per-capita poverty, i.e., poverty rates among children are underestimated by 2–7% points when intrahousehold allocation is ignored (this result is comparably smaller than the findings for Côte d’Ivoire where child poverty is underestimated by approximately 14–23% points, cf., Bargain et al., 2014). Thus, the naïve per-capita measure paints a relatively optimistic picture of child poverty and ignores the possibility that resource sharing is skewed in favour of adults in larger households (expenditure per child decreases with the number of children also as in Bargain et al. (2014) and Dunbar et al. (2012)). Alternatively, the relative need of children is too high in our measure I. As noted above, for children to have a similar poverty rate as adults overall, the poverty line for children must be reduced to around 40% of an adult’s, i.e., 20% of the minimum requirement of a couple. In this measure II (which can be compared to measures I and III but not to per-capita measures), child poverty rates become more similar to mothers’ poverty rates but are still much higher than men’s poverty rates after adjusting for scale economies. Finally, note that our model does not explicitly account for economies of scale among children (these are normalised to 1). The main reason is that identification is difficult as we do not observe children in two states that are pertinent for assessing economies of scale (living alone and living with parents). Nonetheless, if there are substantial economies of scale among children, then poverty rates reported here might be an over-estimate. In view of this, our poverty measures can be viewed as an upper bound estimate of children’s poverty rates. Below we provide additional results for estimated resource shares and draw some cross-country comparisons. 5.2 Additional results 5.2.1 Sensitivity to the choice of the child gender variable In the previous models, we used the proportion of male children to examine if parents exhibit gender preference in the allocation of resources to children. Here, we check the sensitivity of our results to the choice of the variable used by estimating a series of models which use a dummy capturing the gender of children by birth order, i.e., gender of the first, second and third child. The dummy is equal to 1 if the gender of a child is male and 0 otherwise. The corresponding resource shares and scaling factors are presented in the Appendix Table A.3. We find that shares allocated to women, men and children are not significantly different from the shares obtained in the baseline model (Table 3). This stability of results extends to economies of scale, and hence indifference scales, which are of the same order. Parameter estimates for children’s shares are presented in Table A.4. We see that the gender of the first child is significantly and positively related to the share allocated to children. Thus, if the first child is male, the resource shares allocated to children will increase by 20%. This finding is at odds with the result from the baseline model suggesting that the proportion of male children is positively but insignificantly related to children’s shares. Similar to our baseline results, we find that gender of the second and third child does not have a significant effect on children’s resource shares. Thus, parents’ resource allocation appears to be sensitive to the gender of the first child only. Given the mixed results from the different specifications, we opine that the evidence of child gender preference in resource allocation is not compelling. 5.2.2 Sensitivity to the household type of reference In all models presented thus far, single men and women were used as the demographic group of reference. It is important to note that married women or men could potentially have systematically different preferences from single women or men even after controlling for observed characteristics. In this case, our estimates which rely on the use of single men and women as the reference group might be biased. To assess the sensitivity of the results to the choice of reference group, Table A.5 in the Appendix presents results from a model which is closer in spirit to Dunbar et al. (2013). This model termed the ‘unitary couples’ restricts the sample to couples (with or without children) only, and uses couples without children as the reference category. This is in line with the Rothbarth’s approach which relies on adult clothing to identify children’s shares while leaving sharing among adults unspecified (the couple is ‘unitary’). Thus, the sharing function is cast in such a way that only enables the identification of parents’ versus children’s shares. Reassuringly, adult and child resource shares obtained from this model are quite similar to those obtained from our baseline model. We also estimate the Rothbarth-Gronau model which is the same as above (unitary spouses) but ignores economies of scale. The estimated children’s shares are smaller compared to those obtained from the ‘unitary couples’ model. For instance, with the latter, a child (three children) receives 21% (32%) of total household resources compared to 17% (24%) with the Rothbarth-Gronau model. The underestimation (overestimation) of children’s (parents’) shares in the Rothbarth-Gronau approach may be attributed to the fact that parents are not compensated for economies of scale. A similar bias is obtained for Côte d’Ivoire (Bargain et al., 2014). Overall, based on the robustness checks, our findings are fairly stable across models. 5.2.3 Cross-country comparisons We have already provided numerous comparisons of our results with those from aforementioned studies on Malawi and Côte d’Ivoire. To complete this comparison and extract possible regularities across different settings, we present in Table 6 the main statistics from all three studies regarding estimated resource shares. Recall that Malawi and Côte d’Ivoire are much poorer countries than South Africa, yet the latter is characterised by extremely high inequality and we focus on the subgroup of Africans who actually show larger poverty rates than the rest of the population. Table 6: Estimated Resource Shares for South Africa and Other Developing Countries South Africa Côte d’Ivoire1 Malawi2 Childless couple Women 0.447 (0.067) 0.517 (0.071) – – Men 0.553 (0.067) 0.483 (0.071) – – Couple with one child Women 0.360 (0.064) 0.420 (0.075) 0.363 (0.042) Men 0.446 (0.072) 0.392 (0.086) 0.400 (0.045) Children 0.195 (0.083) 0.188 (0.114) 0.227 (0.036) Children (unitary couple) 0.213 (0.053) 0.219 (0.384) Couple with two children Women 0.325 (0.068) 0.401 (0.081) 0.221 (0.043) Men 0.403 (0.080) 0.375 (0.091) 0.462 (0.051) Children 0.272 (0.111) 0.224 (0.134) 0.317 (0.045) Children (unitary couple) 0.261 (0.062) 0.276 (0.578) Couple with three children Women 0.283 (0.075) 0.380 (0.088) 0.176 (0.044) Men 0.350 (0.090) 0.355 (0.098) 0.466 (0.053) Children 0.367 (0.141) 0.265 (0.156) 0.358 (0.050) Children (unitary couple) 0.315 (0.075) 0.341 (0.795) South Africa Côte d’Ivoire1 Malawi2 Childless couple Women 0.447 (0.067) 0.517 (0.071) – – Men 0.553 (0.067) 0.483 (0.071) – – Couple with one child Women 0.360 (0.064) 0.420 (0.075) 0.363 (0.042) Men 0.446 (0.072) 0.392 (0.086) 0.400 (0.045) Children 0.195 (0.083) 0.188 (0.114) 0.227 (0.036) Children (unitary couple) 0.213 (0.053) 0.219 (0.384) Couple with two children Women 0.325 (0.068) 0.401 (0.081) 0.221 (0.043) Men 0.403 (0.080) 0.375 (0.091) 0.462 (0.051) Children 0.272 (0.111) 0.224 (0.134) 0.317 (0.045) Children (unitary couple) 0.261 (0.062) 0.276 (0.578) Couple with three children Women 0.283 (0.075) 0.380 (0.088) 0.176 (0.044) Men 0.350 (0.090) 0.355 (0.098) 0.466 (0.053) Children 0.367 (0.141) 0.265 (0.156) 0.358 (0.050) Children (unitary couple) 0.315 (0.075) 0.341 (0.795) Notes: Standard errors in parentheses. 1Source: Bargain et al. (2014). 2Source: Dunbar et al. (2013). Results for Côte d’Ivoire show more balanced shares of resources among adults in childless couples (the study on Malawi does not include it as it is the reference demographic group used for identification. The sharing pattern in couples with one child is very similar in South Africa and Malawi, slightly more in favour of women in Côte d’Ivoire. When considering couples with two and three children, South Africa seems to hold an intermediary position between the other countries, with large gender imbalance in favour of men in Malawi and more balanced sharing in Côte d’Ivoire (always slightly skewed in favour of women). In fact, as stated above, the difference in adult shares is only significant in Malawi, both because of a larger gender gap and of more precise estimates. Child shares in South Africa are in line with findings from other African countries, again in-between the estimates of these two countries for families with one and two children. We turn back to this point below. An important potential caveat that might limit the relevance of this comparison pertains to the factors that may lead to heterogeneity in the estimates of resource shares across countries, beyond the cultural and institutional drivers of behavioural differences in resource sharing rules across contexts. There are at least three such factors: (a) data / measurement; (b) the sample composition of the households (e.g., heterogeneity in distribution of income, socio-economic characteristics of the households); (c) specific empirical model and research design(s) used to estimate resource shares. Regarding (a), irregularities in our cross-country comparison could be partly due to the use of different data sources: the 2010/11 IES for South Africa, the 2002 Côte d’Ivoire Living Standards Survey, the 2004/5 Malawi Integrated Household Survey. The data are based on non-standardised country specific survey instruments hence, we cannot rule out heterogeneous measurement of some variables used in empirical models, although we tried to establish consistency in the case of South Africa. Regarding (b), another potential source of anomaly is indeed the sample composition of households across countries. The main difference is that these are all rural agrarian in Malawi, at least 48% rural in Côte d’Ivoire and less than 50% rural in South Africa. The proportion of rural households in a country negatively correlates with household welfare so this situates South African and Ivoirian households better than those in Malawi.15 Yet, these differences are not specifically due to the samples at use. World Bank estimates based on the United Nations ‘World Urbanization Prospects’ point to a rural population of 84% in Malawi compared to 35% in South Africa and 45% in Côte d’Ivoire. Possibly entangled with these factors is the effect of more cultural aspects and notably the role of patriarchy on differences in resource shares for Malawi and South Africa (despite their de jure gender equality statuses). For Malawi, patriarchy resonates well with male dominance underlying the configuration of traditional non-urban households—which allocate a large share of resources to men. However, the extent of patriarchy and male superiority is, presumably, more diluted in South Africa, related to the fact that South African men and women are relatively more educated and urbanised. However, underneath these ‘modern’ traits is ethnic diversity and pockets of patriarchy which define the African sample, and hence slightly larger resource shares for men. That Ivorian women have larger resource shares than men remains unexplained in the analysis as the behaviour is atypical given that the society is not free from patriarchy. As stated above, much has to do with the difficulty to identify precise estimates of intra-couple sharing—which brings us to point (c). Despite its generalisation, the Rothbarth-type of approach used in the three studies provides solid identification mainly regarding the parent-child sharing, possibly less so concerning the male-female sharing within the couple. Hence, we return to Table 6 to investigate the observed differences in children’s shares. It seems that for all three countries, child shares are similar for the first child. They tend to be relatively smaller in Côte d’Ivoire for larger families, especially in comparison with estimates for Malawi. Some of it might be due to modelling choices, notably the fact that for the latter country, Dunbar et al. (2013) use a slightly different identification strategy. To improve on the comparison between studies in that respect, we report in Table 6, below children’s resource share, the share that they obtain from estimations based on couples only (childless couples now serve as the reference group) and when ignoring sharing among parents (‘unitary couples’). Not relying on single individuals and assuming stability of preferences across people living in the household (men and women) brings the model closer to Dunbar et al.’s identification strategy. In this case, we see that children’s shares become much more comparable across countries. It especially makes estimates for Côte d’Ivoire more similar to those of the two other countries. This similarity is striking and may indicate—to the extent that aforementioned caveats do alter these results—relatively more universal results regarding the allocation of resources between parents and children compared to that among adults. 6. Conclusion Using a collective model of household behaviour which accounts for parental bargaining and jointness in consumption, this paper estimates the household resource sharing process, economies of scale and, subsequently, the degree of individual inequality and the incidence of individual poverty. We find that usual bargaining factors—like the difference in spouses’ age and education—significantly affect the share of household resources accruing to women. Mother’s employment status has a considerable effect on children’s resource shares. Further, we find moderate economies of scale, benefiting mostly men and increasing with family size. We find a gender imbalance among spouses, yet not statistically significant, but no compelling evidence of gender differences among children. Cross-country comparisons of within-household resource shares situate African women’s between their Ivorian and Malawian counterparts’. Child shares are reasonable for the first child but decrease strongly with family size, which is in harmony with findings in precedent studies. From these resource shares, we derive original individual poverty measures. Poverty incidence results display gender sensitivity to resource allocation: women are more likely to be poor than men. Arguably, broader gender inequality trends reported in the country are somewhat traceable to households. We also note that a considerable proportion of families lack resources to meet the basic standard of living—mainly to the disadvantage of children in multi-children households, who appear to be more vulnerable than adults. Adjustments for economies of scale reduce poverty rates among adults by a large margin. These results suggest that ignoring intrahousehold distribution of resources and joint consumption leads to an inaccurate poverty profiling in South Africa. Although this study provides some important insights into the intrahousehold allocation of resources in South Africa, it is not without limitations. The model estimated herein places some stringent requirements on the data, i.e., the use of nuclear households and single men and women. Given the notion of ‘ubuntu’ among African households, we lose a substantial portion of our sample to extended families. Thus, our analysis is focused on a more tightly knit set of families which is a selected sample. Future studies should endeavour to extend the model to a wider range of family types prevalent in African societies. In addition, the model does not explicitly model economies of scale among children due to identification issues. Again future considerations on this matter are essential for a more complete assessment of household behaviour and individual welfare. Supplementary material Supplementary material is available at Journal of African Economies online. Acknowledgements We would like to thank Zaki Wahhaj, Michèle Tertilt as well as participants at the 2015/16 UNU-WIDER/University of Namur Gender and Development workshops and the 2015 MASA conference for useful advice. This research was originally commissioned by UNU-WIDER in Helsinki, within the Gender and Development research project: https://www.wider.unu.edu/project/gender-and-development. Footnotes 1 In some other context like the Muslim bride price, this type of scheme may actually help women, serving as an insurance against no-fault divorce (Ambrus et al., 2010). 2 This approach has been operationalised in several studies using the estimation of systems of Engel curves to retrieve the cost of children or to test for gender discrimination among children, for instance Deaton (1989) or Haddad and Hoddinott (1994). The difference here is that we integrate these measures in a structural framework and allow for more flexibility than in the original Rothbarth approach, with the modelling of scale economies and intrahousehold bargaining. 3 The idea of combining data on people living alone and in couples to retrieve the complete resource sharing rule is applied in Couprie (2007), Lise and Seitz (2011), Browning et al. (2013) and Lewbel and Pendakur (2008). Other assumptions are made in Dunbar et al. (2013). 4 Another aspect is that consumption may be joint from one spouse’s perspective but not from the other’s, depending on the balance of power. Assume for instance that the husband has the say and decides about the level of expenditure on the dwelling, then it will be private to him but joint to her (see Donni, 2015). 5 Note that identification requires regularity conditions to be satisfied, namely that the second order derivative of the basic budget share with respect to log expenditure be different from zero, at least for some values of x. 6 See also Bargain and Donni (2012) and Bargain et al. (2014). These basic budget share equations are consistent with a generalisation of the Piglog indirect utility function (Banks et al., 1997). 7 Households with more than three children are primarily composed of older children. Children above 14 pose problems for the identification strategy since their clothing expenditure are counted as adults’. 8 This consists of single men who report expenditure on female and child clothing, single women reporting expenditure on male and child clothing and childless couples who report expenditure on child clothing. 9 Also, education and health expenditure relate to risk and dynamic choices, which are better excluded in our static framework under certainty. 10 As highlighted above, we have also checked for endogeneity of total expenditure and for the non-linearity of budget share equations in log expenditure (especially for adult goods, i.e., a necessary condition for identification as mentioned above). For each household type, reduced-form budget share equations were regressed on all the covariates used in the structural version of the model (including log total expenditure and its square) and the Wu-Hausman residual. The coefficient of the Wu-Hausman residual was significant in several cases, suggesting that endogeneity of expenditure is an issue and that this residual should be included in the structural Engel curve estimations. The coefficients on log expenditure and its square in adult clothing equations are significant and show a quadratic pattern in most subsamples. 11 With model II in particular, we notice that the difference between women’s and men’s shares of total expenditure is only slightly more marked. It means that incorporating economies of scales that are specific to both spouses, as in the baseline model, explains only a fraction of the differences in women’s and men’s expenditure on clothing observed in the raw data. 12 Note that these results would not necessarily translate to inequality in couples if identification was based on goods that can generate difference in needs (for instance food, if men do need more calories than women). And even though, what matters for identification is the double difference between men and women in couple with respect to men and women living alone. In particular, difference in prices for male and female clothing would apply to both singles and couples so that it would not explain the unequal resource sharing we observe here. 13 This is line with Deaton (1989) who found no evidence of child gender bias in the overall treatment of boys and girls in Côte d’Ivoire, using adult equivalence outlay ratios and data for the year 1985, or Bargain et al. (2014) who reach the same conclusion for Côte d’Ivoire using the same approach as in the present paper. Bhalotra and Attfield (1998) consider food allocation among children in Pakistan and also point to the absence of gender imbalance among children. 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Published by Oxford University Press on behalf of the Centre for the Study of African Economies, all rights reserved. For Permissions, please email: firstname.lastname@example.org
Journal of African Economies – Oxford University Press
Published: Mar 1, 2018
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