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Heterogeneity and household behaviour: discerning the consequences of intra-household resource allocations

The findings presented in tables 1 to 3 are of value to policy-makers. While certainly not conclusive regarding the effects of changes in wage rates on schooling and non-market time and of the effects of changes in food prices on health, they do confirm the value of estimating the person-specific "demand equations" (7) and the importance of data sets containing variability in wage rates, prices, and measures of outcomes of interest to policymakers. These reduced-form estimates, however, are only relevant to the populations studied; in particular, they are conditional on the specific technological relationships characterizing household production (and agricultural production) in those populations. Moreover, it is obviously useful to understand how price changes alter health - how the intra-family distribution of food and other inputs varies across individuals and how these resources directly affect health. To better anticipate how the allocation of time and goods within the household will respond to price and wage changes induced by new programmes or policies, and how foods and other inputs directly alter health or other outcomes, requires knowledge of the technological substitution possibilities in, and other characteristics of, household production, depicted in relation (1) of the household model.

Table 3, Food price effects. aggregate household nutrient consumption, and the incidence of illness among household heads and their wives Indonesia^a

a. For a list of all included variables and description of data. see Pitt and Rosenzweig (1985).
b. Absolute values of asymptotic t-values beneath coefficients.
Source: National Socio-economic Survey, 1978.

Knowledge of the "technological" relationships between family resources and such outcomes as the health and earnings potential of children is valuable not only for improving understanding of the constraints conditioning household behaviour but also for educational interventions aimed at helping households better to allocate resources (when and if their understanding of such relationships is deficient). Information about which foods or other household resources are most "productive" with respect to health, how the timing of childbearing and family size directly affect the survival of children, and how investments in schooling affect the returns on market and non-market activities must come from estimates of the effects of household allocations on such outcomes. Indeed, the estimation of the effects of household resources on the survival, health, and well-being of children has been a central concern in the demographic, economic, and medical literatures (cf. Heller and Drake, 1979; Olsen and Wolpin, 1983; DaVanzo et al., 1983). One of the potential problems in obtaining estimates of the effects of such household-controlled inputs as breast-feeding, foods, schooling, and the use of medical services on measures of child health or indicators of earnings potential, however, is the existence of factors known to or affecting parents but unobserved by the researcher. Variations in such unobserved factors (heterogeneity) across households and across individuals within households in the sample population may result in misleading estimates of the causal relationships between parental choices and observed outcomes. Yet few studies have been attentive to this problem (cf. Engle, this volume).

There are two distinct sources of heterogeneity, with different implications for statistical treatment. First, there may be across-household variation in the environment in which allocative decisions are made - mosquito infestation, sanitary conditions - or in the inherent healthiness or abilities of parents, some of which is transmitted genetically to offspring. If parents take into consideration these household factors in their allocative decisions - for example, if households in healthier environments use fewer medical services - then the observed association between variations in family inputs and measures of outcomes will not correctly measure their consequences for those outcomes.

A second source of heterogeneity arises from variations in the inherent qualities of individuals within a family. As is indicated in the resource allocation "rule" (6), differences among individuals in healthiness or skills (µⁱ in the model (1)) will generally influence resource allocations across family members.(5) Yet little empirical evidence exists on how resources are allocated across family members as a function of their "endowments." Moreover, without the imposition of additional structure on the household model, it is impossible to know a priori whether more-endowed or less-endowed individuals will receive higher levels of household resources (cf. Engle, this volume). Therefore it is difficult to anticipate how estimates of resource effects which do not take into account intra-family heterogeneity and allocative behaviour will be biased.

To see the trade-offs implicit in the household model, consider a household containing two children with unequal abilities; specifically, assume that one child is characterized by a higher return on schooling than another (a higher rⁱ in relation (2) of the model). If parents provide schooling equally across the children, their offsprings' earnings will be unequal; if parents provide more schooling to the more able child (until marginal returns are equalized), average and total child earnings will be maximized, but earnings inequality will be exacerbated compared to the equal-input allocation rule. If the parents equalize outcomes (earnings in this case), the less-endowed child receives more schooling. The average and thus total earnings of the offspring will be reduced compared to the equalinput or earnings-maximizing allocative rules.

In the absence of transfers among siblings when they become adults, or with parents caring about individual earnings potential (rather than just the total income of their offspring) as in (3), the household faces a trade-off between equality and efficiency in the intra-family distribution of its resources. How it resolves this trade-off will determine the sign and magnitude of the biases in estimates of the effects of household resources. If, for example, more (less) food is allocated to healthier children or more (less) schooling is allocated to higher-ability children, then associations between food intake and health or schooling and earnings will overstate (understate) the true causal effects of these inputs. Behrman and colleagues (1982) show empirically, based on United States data and a particular configuration of the household model, that parents do not allocate schooling resources across children to maximize average children's earnings; parents are inequality-averse (cf. Behrman, next chapter).

The association between the endowments of individuals and the resources they receive from the family depends on both the characteristics of the technology and the household welfare function. In the schooling case, it was assumed that individuals with higher ability received higher market earnings for given invested skills. However, medical services may be most productive when allocated to less healthy individuals. In that case, there is no trade-off between outcome (health status) equality and efficiency. Moreover, estimates of the efficacy of medical service use inattentive to allocative rules and heterogeneity will then be too low, as found by Rosenzweig and Schultz (1983) in our study of the consequences of pre-natal care for birth-weight outcomes.

One relatively straightforward estimation procedure that can be (and has been) used to eliminate the biases caused by intra- and inter-family heterogeneity relies on the input demand equations (7). The right-hand-side variables in (7) are natural instruments for identifying the technology of production, since variations in prices and in the exogenous determinants of market wage rates are presumably uncorrelated with family endowments (in the absence of significant selective migration), and influence outcomes only by affecting the intra-family distribution of resources. Consistent estimates of the relationships between family resource distributions and outcomes can therefore be obtained by estimating the demand equations first, and then estimating the production functions using predicted allocations based on the demand estimates.

How important are these sources of bias? Rosenzweig and Wolpin (1988) compared estimates of the effects of various household control variables - the timing, spacing, and number of children; the use of inoculations; breast-feeding; and food consumption - on the age-standardized weight of children within six months of their birth, using different estimation procedures. In order to isolate within-household and acrosshousehold sources of heterogeneity we used information from households that had at least two children born within a seven-year period, taken from a probability sample of 104 households in Candelaria, Colombia. Table 4 reproduces estimates of the parameters of the normalized childweight equations obtained from procedures that (1) ignored all forms of heterogeneity (OLS); (2) took into account only heterogeneity across families (family fixed effect or FFE); and (3) took into account both intra -and inter- family heterogeneity (two-stage least squares or TSLS) using parental schooling, programmes, and occupation as instruments.

The FFE method, which "corrects" for inter-family heterogeneity, and the TSLS method, which additionally avoids biases associated with intra-family heterogeneity, yield different results. These also differ from results obtained using the OLS procedure. In particular, while the OLS estimates suggest that breast-fed children experience (marginally significantly) greater weight gain, the breast-feeding coefficients are neither positive nor significant when estimated with either FFE or TSLS methods. This result does not necessarily imply that breast-feeding is ineffective (since the effect of breast-feeding depends on its duration and intensity, and breastfeeding may enhance child survival).

Rather, the estimates suggest that inattention to heterogeneity may lead to an overstatement of the effects of breast-feeding incidence on children's weight. Conversely, the effects of household food consumption per capita, and to a lesser extent of inoculations, appear to be understated using either OLS or FFE methods, which ignore intra-household heterogeneity. Neglect of heterogeneity across and within households also appears to lead to an overestimate of the persistent effects of birth order and birth intervals on post-birth weight. While many of the individual coefficients are not measured with much precision, heterogeneity both within and across the sample house holds appears to be affecting the intra-household and inter-household variations in the inputs and thus the estimated coefficients in this sample of children.

Table 4. Household resource allocations and the log of weight-for-age: children in Candelaria, Colombia ^a

a. For data description and details of estimation, see Rosenzweig and Wolpin ( 1988, forthcoming).
b. Endogenous variable.
c. Log of variable.
d. Absolute values of tratios beneath regression coefficients.
e. Absolute values of asymptotic t-ratios beneath coefficients.

Finally, determination of how the household allocates resources according to the endowments of individuals within the household is not "just" an estimation issue. These household allocative rules have important long-term consequences for inequality associated with particular programme or policy interventions. An increase in schooling opportunities, for example, may benefit the more able and thus could exacerbate earnings inequality. A health programme could reduce disparities in healthiness in the population, depending on the inter- and intra-household distribution of resources and on the nature of the household technology.

CONCLUSION

In this paper, I have briefly reviewed the implications of economic models of the household in order to assess how programme interventions affect the consumption of or investments in individuals who are members of collective decision-making groups or households. While the models discussed ignore many of the problems associated with collective decision-making, richer, more detailed models will likely be characterized by many of the features present in the existing economic models of the household that view the household as maximizing a given welfare function. Such models imply that policy-makers must pay particular attention to the interdependence among household members. Interventions aimed at encouraging particular activities or augmenting the welfare of particular individuals will have cross-effects, will affect other individuals, and may induce other activities, perhaps with less desirable results. These cross-effects come about as long as some resources received by individuals are pooled and reallocated within the collective entity.

A better understanding of how households allocate their resources will no doubt come when the models of household decision-making are imbedded in a broader framework which explains household size and composition and how households form and break up. Work on improving our understanding of the benefits of the family as an organization has already begun (Cain, 1981; Kotlikoff and Spivak. 1981; Rosenzweig and Wolpin, 1985, 1988). but has not yet been integrated with models of intra-household resource allocation.

Despite the limitations of existing models of household behaviour, it would appear that the current binding constraint on knowledge is the state of existing data. The theoretical framework provides a clear indication of the kinds of data needed for improving our knowledge in order to anticipate the consequences of interventions, given intra-household allocative behaviour; few data sets meet these requirements.

First, the models imply that information needs to be elicited on sources of income, by individual, with particular attention to wage rates (cf. Rogers, chapter 1, and Appendix). Most surveys lump all resources together, even though family income is itself an outcome of household decisions and even though different sources of income have significantly different effects on allocations. Second, price variability is critical for understanding how allocations and outcomes vary in response to interventions. Detailed information in one price-income-endowment environment, no matter how accurate, cannot tell us anything about how behaviour changes when there are alterations in the environment in which households exist, yet that is exactly what programmes are designed to do. Third, given price variability, a cost-effective means of obtaining information on the effects of interventions is to obtain information on outcomes of interest. If policy-makers are concerned about health, morbidity, or schooling, then these outcomes should be measured as a priority. Yet many surveys concentrate their efforts on collecting data on household inputs rather than on individual outcomes. Information on household food consumption or time allocation is useful, but cannot be used to estimate household technology (production functions) or to make welfare judgments without measures of the ultimate consequences of those inputs. Policy makers as well as researchers must make the decisions about which ultimate consequences are of interest. Poor integration of survey design and modelling so far have been critical impediments to knowledge.

NOTES

1. I do not attempt here to define precisely the decision-making unit. In principle, any collection of individuals who pool resources and/or whose activities are interdependent could qualify as the relevant entity. Thus, co-residence is neither a necessary nor sufficient condition for the existence of a "household." One might operationalize this concept by the following definition: person i and person j are in the same decision-making unit if person i's (i's) resource allocations are not independent of person j's (i's) income or earnings.
2. There may be an additive endowment effect as well. To simplify, I omit a discussion of the distinction between additive and multiplicative endowments.
3. The household decision-makers may also care about whom household members marry or the kind of households of which they become members. These considerations are discussed in Behrman and Wolfe (1983) and Rosenzweig and Boulier (1984).
4. Another difference is that the Philippines data provided information on hours of work for children aged ten and above, while the Indian data only provided information on children's labour-force participation. The Philippines' results indicate the existence of backward-bending supply (hours) "curves" for children. "Own" wage-rate effects on participation probabilities must be positive, of course, as they are in the India data.
5. For example, it is well-known that an infant's intake of breast-milk depends on its ability to suck; immature or ill infants may thus be breast-fed less or not at all, leading to an upward bias in the estimation of the effects of breast-feeding on infant survival or nutritional status.

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