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3. Peeking into the black box of economic models of the household

Economics Department, University of Pennsylvania, Philadelphia, Pennsylvania, USA


An organizing framework is essential for asking what empirical dimensions of reality are relevant and for interpreting data about that reality. The economic model of the household, despite its limitations, some of which are noted by Rosenzweig (1984 and this volume), provides a very useful framework for such purposes. It has provided many important insights, particularly regarding the importance of prices in addition to income effects, the difficulty of signing the impact of many exogenous changes, the possibilities of substitution among members of a household within and across generations, the role of overall resource constraints (including those of time), and the influence of often unobserved endowments (or heterogeneities in Rosenzweig's terminology). For empirical work it points to the importance of data on wages for individuals and on prices that the household faces, as well as on endowments of individuals and households. It also suggests that data on individual inputs (e.g. nutrition) that are determined within the household may be difficult to obtain, in part because of intra-household substitution and transfers. Therefore, as Rosenzweig points out, data on the related outcomes (e.g. health measures) may be much more cost-effective to obtain.

But it should be noted, particularly given Rosenzweig's emphasis on the importance of wage data, that if wages depend on consumption of nutrients and other health-related inputs, as Leibenstein (1957) long ago conjectured and as some recent studies report (e.g. Behrman and Deolalikar, 1988; Deolalikar, 1988; Sahn and Alderman, 1989; Strauss, 1985, 1986), then wages are endogenous and do not appear in the reduced forms. Thus, the appropriate representation of the opportunity cost of time may be much more complicated and much more difficult to identify empirically than Rosenzweig suggests.

Furthermore, empirical applications of the economic household model as Rosenzweig describes them basically treat the household as a black box,' in the sense that observed outcomes respond within a reduced-form framework to exogenous changes in market prices and other variables. In this discussion I shall peak into that black box, first empirically and then theoretically.


The reason why most empirical economic applications' including examples given in Rosenzweig's paper, treat the household as a reduced-form black box is that the data requirements make any other option difficult. At times, however, special data in combination with a theoretical framework can permit a glimpse inside the household black box.

To illustrate how this works, I summarize recent work in which I have been involved concerning the nature of household allocations among children.2 Assume that the parents of the children behave as if they are maximizing (subject to constraints) their preferences defined over the distribution of expected outcomes (e.g. earnings or health) among their children and that the expected outcomes for each child depend on the parental allocation of inputs (e.g. schooling, time, or nutrients) and on child-specific endowments (e.g. genetic characteristics).3 Two important questions about the parental preferences can then be answered with a specific version of the economic household model and special sibling data on inputs and outputs.

Fig.1.Alternative parental preferences between expected outcomes for children 1 and 2.

First, to what extent do parents allocate resources so as to compensate for or to reinforce inequalities across children in endowments? Figure I illustrates three alternatives for the preference curves of parents between expected outcomes for two children. At one extreme, the preference curve is L-shaped or Rawlsian, showing that parents are concerned only about the worst-off child. They devote all of their resources to that child until the expected outcome for that child is as good as that for the next worst-off child. At the other extreme the preference curve is linear, so that parents follow a pure investment model by allocating resources to their children so that the highest total returns are obtained, with no consideration about the distribution of outcomes. Among all of the intermediate possibilities, there is one of particular interest (which economists call the Cobb-Douglas case), because for this degree of curvature parents are neutral, neither reinforcing nor compensating inequalities in child endowments.

Second, to what extent do parents favour one type of child (i.e. designated by sex or birth order) over others in the sense that an equal outcome is valued more highly for the favoured type child than for others? In terms of figure 1, this question refers to whether or not the parental preference curve is symmetrical around the 45 ray from the origin. If it is symmetrical, as in figure 1, the parents have equal concern, independent of the type of child.4 If it is not symmetrical, as in figure 2, the parents weigh equal expected outcomes more heavily for one child than for the other (in this case, more for child 1).

With collaborators, I have estimated the curvature and symmetry around the 45 line of parental preferences based on sibling data from samples for the United States and for rural south India. For the United States the expected output data related to adult earnings and the input data to schooling levels for two different recent generations. For India, the expected output data are health outcomes (as indicated by anthropometric measures) and the input data are nutrients for both the lean and surplus seasons (as defined by food availability).

For the United States, the estimates suggest that parental preference curves are shaped approximately like the Cobb-Douglas case for both generations. This implies significant parental inequality aversion and behaviour far different from that of a pure investment model, but with close to neutrality concerning the compensation or reinforcement of endowment differentials.5 Parents also slightly favour older children and girls in the sense that they weigh equal outcomes for such children more heavily than they do for younger children and boys.

Parental preferences that weight eqal expected outcomes more heavily for child 1than for child 2.

For India, the estimates suggest about neutral (Cobb-Douglas) curvature of parental preferences in the surplus season when food is relatively abundant, but much closer to a pure investment strategy in the lean season when food is in short supply.6 Moreover, the allocations suggest preference for boys over girls and for older over younger children in the lean season. The male preference result persists if differential (by gender) expected labour-market wages are introduced, thereby suggesting that the greater allocation of nutrients to boys is not due solely to higher expected labour-market returns to investment in boys (than in girls), as is emphasized in Rosenzweig and Schultz (1982). These results do not differ significantly between nuclear and extended households. But the weights on outcomes of children whose mother is not in the household are systematically smaller than for those whose mother is present, consistent with the critical role of mothers in the food allocation process that has been emphasized by Engle (this volume) and others. Thus, particularly in the lean season, when food supplies are relatively limited, the results suggest that the most vulnerable the less well-endowed, the younger, the girls, and the motherless- receive systematically fewer nutrients.

Such studies are valuable in better understanding intra-household allocation, but the data requirements are substantial. For the United States case, information on adult siblings was required; for the Indian study, information on individual nutrients consumed by all siblings. Both types of data are expensive to collect, which precludes widespread replication of these and other studies that empirically look inside the household through large representative social-science samples.

I therefore agree with Rosenzweig that, for many purposes, the most cost-effective empirical approaches may focus on individual outcomes that are determined by intrahousehold allocation processes as conditioned by changes outside the household, in markets and elsewhere, without explicit representation of the intra-household allocation process. But for some purposes, such as in the studies that I review here, such reducedforms approaches cannot provide the necessary information.


A theoretical peek into the black box of economic household models

Several assumptions of the economic household models summarized by Rosenzweig bother many non-economists, and indeed some economists. I will now briefly discuss some of these.

Existence of a Unified Household Preference Function

Rosenzweig explicitly posits that households act as if such a function is being maximized. Others, as Rosenzweig notes and Engle emphasizes in her chapter, question whether such an assumption does not do violence to reality, since they perceive the actual intrahousehold allocations to be the outcome of bargaining positions based on power.

For reduced-form relations tying observed outcomes to exogenous change (but collapsing intra-household allocations into the parameters) estimated from the existing data on which Rosenzweig concentrates, however, it is not clear that substituting other stable household allocation rules would make any difference as long as the allocation procedure did not depend upon additional variables. Reduced forms still would result, indicating that the observed outcomes depend on the exogenous changes. Within such reduced forms, for example, it is not possible to identify to what extent the coefficient on the women's labour-market wage is due to reallocation in response to changes in her opportunity cost of time in a model with a unified preference function or to her altered influence on allocation in a bargaining framework. Only if the alternative frameworks led to different predictions would such identification be possible. To my knowledge, alternative models that permit such identification with data typically available have not yet been developed.

One can conceive, however, of experiments which result in data that can be used to distinguish between a unified household preference function and a bargaining model. For example, transfers could be distributed randomly to different household members and empirical tests could be conducted to see if who received such transfers made a difference. But care would have to be taken to assure that the distribution of such transfers was orthogonal to (i.e. statistically independent of) individual characteristics such as schooling or number of children that may be associated with an individual's human capital and opportunity cost in terms of time. Existing datasets of which I am aware do not have this property. Instead, transfers have been made on the basis of factors such as number of children, income, or family structure that are likely to be associated with the opportunity costs of time.

Of course, all this is not to say that the unified preference approach is correct - it is empirically no more so (nor less so) than the alternatives. Nor is it my intent to discourage the development of alternative models with testable predictions or of alternative datasets with the necessary properties to permit testing between alternatives. To the contrary, such developments would be most welcome, since they could shed useful light on changes in household structures and household formation and dissolution. But at this time, no one has proved that there is a better way of looking at reduced-form relations that result from intra-household allocation.

Existence of Stable Preferences

Economists tend to assume that tastes are fixed, though some economists (e.g. Easterlin et al., 1980) have questioned whether tastes might not be endogenous. Suppose that the latter were true. Would that affect conclusions of the sort that Rosenzweig derives from his empircal explorations?

The answer is: it depends. For example, suppose that tastes depend on schooling and that Rosenzweig includes the woman's schooling in reduced forms for health outcomes because of widespread hypotheses that the woman's schooling positively affects household productivity related to health, but he does not specify an actual dependence of tastes on the woman's schooling. Despite this misspecification, the reduced forms have the correct variables and the interpretation of the magnitude of the impact of a change in the woman's schooling on health is unaffected. The only problem may be in interpretation - for example, if the impact of the woman's schooling is interpreted to be solely a productivity effect.

Suppose, alternatively, that tastes depend on some variable that is not in Rosen-zweig's reduced forms. If this variable is correlated with the included variables, then the failure to include it causes omitted variable bias in the variables with which it is associated, since they partially represent the omitted variable in addition to their own effects. 7

Constrained Maximization as a Representation of Behaviour

Some maintain that maximization is not a good representation of behaviour, because households (or individuals) are constrained by cultural norms or because they do not adjust to every chance for slight gain (due to the costs of adjustment), but instead "satisfice" by following rules of thumb, for instance. Of course, within Rosenzweig's framework, these possibilities could be incorporated as additional constraints perhaps without changing his reduced forms. If so, these would not alter his basic empirical approach. If not, they could cause biases if the omitted variables were correlated with included ones.

Dynamic Interpretation of Cross-section Estimates

Rosenzweig's estimates of the reduced forms from the economic model of the household generally depend on cross-section associations. Yet the interpretations are dynamic: if one increases this price or expands schooling, then.... Such interpretations may be wrong if there are other dynamic changes that are being held constant in the cross-section (e.g. new technology or changed position of a reference group for norms), or misleading (depending on the time horizons) if there are adjustment costs. Of course, these are the problems inherent in any dynamic deduction from cross-section data, and are not peculiar to studies based on economic household models.


Given the present state of our knowledge, it is pretty dark in the black box of economic models of the household. None the less, Rosenzweig's survey could usefully be extended to show that some peeks inside are possible empirically, as discussed above, although at a data cost which severely restricts replicability. Limited efforts to peek inside theoretically lead to the conclusion that the testing of alternative hypotheses about the functioning of households is indeed difficult, since usually the predictions regarding the reduced forms do not differ for existing data. In such a case, there is nothing to recommend the alternative over the economic household model, or vice versa, except for simplicity. Because of such possibilities, care must be taken in interpretation, because often the identification of the impact of particular variables (e.g. schooling) depends upon assuming away other a priori plausible affects.


  1. A term that Pinstrup-Andersen and Garcia also use in their paper in this volume.
  2. The research presented in this paper was generously supported by a grant from the National Institutes of Health. See in the reference list the citations of which I am author or co-author.
  3. Conditional upon the explicit functional forms utilized, the basic features of the model can be estimated. although the endowments are not observed.
  4. Except at the Rawlsian extreme, equal concern does not mean that parents maximize by allocating inputs to obtain equal expected outcomes for each child. The parents attain the highest possible preference curve subject to the expected outcome possibility frontier. This in turn depends on total resources allocated to the children, the production relations between parentally allocated inputs and endowments on the one hand and expected outcomes on the other, and on the distribution of endowments across children. Since endowments in general are not distributed equally across children, this productionpossibility frontier generally is not symmetrical around the 45 line, and the maximization of parental preferences where the preference curve is tangent to the productionpossibility frontier is not on the 45 line (thus not implying equal expected outcomes across children).
  5. The econometric analysis in Behrman and Taubman (1986) suggests that, due to simultaneity, these estimates probably are biased towards the investment model. If so, actual behaviour may compenstate for endowment differentials rather than be neutral.
  6. The comment in the previous note about simultaneity bias again applies, but the bias is not likely to be large enough, so that the true lean season value is neutral or compensating instead of reinforcing.
  7. There also may be ambiguous private welfare effects since, with endogenous tastes, preferences change with schooling or whatever (see Easterlin et al., 1980).


Behrman, J.R. 1984. Birth Order, Nutrition and Health: Intrahousehold Allocation in Rural India. Mimeo. University of Pennsylvania, Philadelphia, Pa.

-. 1988a. Nutrition, Health, Birth Order and Seasonality: Intrahousehold Allocation in Rural India. I. Devel. Econ., 28(1): 43-62.

-. 1988b. Intrahousehold Allocation of Nutrients and Gender Effects: A Survey of Structural and Reduced-form Estimates. In: S.R. Osmani, ea., Nutrition and Poverty. Oxford University Press, Oxford.

-. 198&. Intrahousehold Allocation of Nutrients in Rural India: Are Boys Favoured? Do Parents Exhibit Inequality Aversion? Oxford Economic Papers, 40 (1): 32-54.

Behrman, J.R., and A.B. Deolalikar. 1988. Wages and Labor Supply in Rural India: The Role of Health, Nutrition and Seasonality. In: D.E. Sahn, ea., Cause and Implications of Seasonal Variability in Household Food Security. Johns Hopkins University Press, Baltimore, Md.

Behrman, J.R., R.A. Pollak, and P. Taubman. 1982. Parental Preferences and Provision for Progeny. J. Poll Econ., 90(1): 52-73.

-. 1986. Do Parents Favor Boys? Internat. Econ. Rev., 27(1): 31-52.

Behrman, J.R., and P. Taubman. 1986. Birth Order, Schooling and Earnings. J. Poll Econ., 4 (3/part 2): S121-145.

Deolalikar, A.B. 1988. Do Health and Nutrition Influence Labor Productivity in Agriculture? Econometric Estimates for Rural South India. Rev. Econ. Stat., 70(30): 406-413.

Easterlin, R.A., R.A. Pollak, and M.L. Wachter. 1980. Toward a More General Economic Model of Fertility Determination: Endogenous Preferences and Natural Fertility. In: R.A. Easterlin, ea., Population and Economic Change in Developing Countries, pp. 81-150. University of Chicago Press for National Bureau of Economic Research, Chicago.

Leibenstein, H.A. 1957. Economic Backwardness and Economic Growth. John Wiley, New York.

Rosenzweig, M.R., and T.P. Schultz. 1982. Market Opportunities, Genetic Endowments and Intrafamily Resource Distribution: Child Survival in Rural India. Am. Econ. Rev., 72(4): 803815.

Sahn, D.E., and H. Alderman. 1989. The Effects of Human Capital on Wages, and the Determinants of Labour Supply in a Developing Country. J. Devel. Econ., forthcoming.

Strauss, J. 1986. Does Better Nutrition Raise Farm Productivity? J. Poll Econ, 94: 297320.

-. The Impact of Improved Nutrition on Labor Productivity and Human Resource Development: An Economic Perspective. Paper presented at the International Food Policy Research Institute Workshop on the Political Economy of Nutrition Improvements, West Virginia, 1985.

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