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Person-specific prices and goods-specific prices

The family not only allocates consumption goods across its members, but determines (a) the time each individual spends in household production, leisure, and earnings activities and (b) the allocation of inputs among production activities. The human capital (health, earnings potential), consumption, and time allocation for each family member thus depends on the prices of all goods, the wage rates of every family member (or the returns to human capital ri of each family member), the endowments and/ or characteristics of every family member, and total family income. Solution of the model yields a set of personand activity-specific "demand" equations for consumption, input, and outcome variables:


where. Policy or programme interventions that alter one of the right-hand side variables in the "demand" equations will thus generally change the intra-family distribution of all resources and outcomes.

Two kinds of "prices" are worth distinguishing. First, there are prices which are specific to goods but not to individuals. A food subsidy/farm policy that induces a change in the price of wheat, for example, affects the relative desirability of wheat compared to other foods and goods for the household but not differentially for individuals within the household. Conversely, there are prices which are specific to individuals but not to activities. A change in the return to human capital (or the wage rate for individual i) affects the relative returns to allocating time to the labour market versus household production/maintenance among family members, but not the relative costs of the different household activities to which each person i allocates his/her time. As a consequence, the model, with few additional restrictions, provides predictions with respect to how changes in goods-specific prices affect the aggregate composition of goods consumed at the household level, but not how these goods are reallocated among family members. The model also provides predictions as to how a change in the value of time (a person-specific price) of any individual family member influences the time allocation of family members across market and non-market activities, but not how the members will allocate their time across household activities. These predictions and their policy implications are discussed in the next two sections.

Wage Rates, the Value of Time, and Time Allocation: Investments in Schooling

As noted, in the unified household model it does not matter in terms of resource allocation to whom in the family income is provided. The source of family income change, however, is critically important. If the source of income growth is an increase in the return on a particular family member's time, for example an increase in the wage rate for member i, then that will induce the family to reallocate resources within and across household activities. In particular, the household will tend to devote less of its resources time and goods - to activities "intensive" in the time of the family member i, whose opportunity cost of time has risen. Moreover, within activities, goods and other family members' time will substitute for member i's now higher-priced time.

Some projects are designed mainly to increase jobs, and many others have employment consequences, even if they are initiated to accomplish other goals. An employment-creation scheme or any project which increases the demand for labour will thus induce withinhousehold reallocations, particularly if the programme raises the labour-market returns of one group relative to another. If the closest substitutes for an individual's time in household activities are other household members' time, then the principal reallocation will occur with respect to the household's pattern of time allocations.

To illustrate the importance of the source of income growth, consider two schemes: a jobcreation programme that increases the labour demand for unskilled, adult women relative to others, and one that augments the demand for skilled women. The first programme raises the value of time of adult women W but not the return to investments in human capital r in the model. If the income effects of such a programme are small, adult women will increase their time allocated to market work and other family members may work less in the market, substituting their time in household activities for that of adult women. Who works less and what the new allocation of family members' time is among activities will depend on household preferences (4) and on the substitutability of different members' time and goods in these activities (1) and (3). If, for example, the time of daughters is considered a better substitute for the time of the mother in home production activities, it is possible that the first (unskilled jobs) programme will reduce the time girls spend in the labour market (and thus their work experience) and in school, while increasing the employment of adult women. Wage rates of women in the longer run may thus decline relative to men as a consequence of the lesser experience and schooling of the next generation of women, because of intra-household allocative responses. These intergenerational effects are elaborated in Rosenzweig (1982).

The second, skill-based, employment scheme has two effects. First, the opportunity cost of adult women is increased, thereby inducing the possible time-allocative effects just discussed. Second, and possibly offsetting these, is the incentive for investments in skills, particularly for girls, induced by the rise in the return on the human capital of women caused by the programme. The within-household cross-wage effects of the job-creation schemes thus depend on: (1) how the jobs affect the relative time costs of family members and the incentives they create for human capital investment; (2) the technology of household production, i.e. substitution possibilities; and (3) household preference orderings.

How important are these "cross-wage" effects on the allocation of family members' time? Many studies of the labour supply of married women in the United States confirm the importance of these effects for labour supply (Ashenfelter and Heckman, 1974). There has as yet been little empirical work on how, for example, mothers, fathers, sons, and daughters interact. Tables 1 and 2 report matrices of estimated "own" and cross-wage effects by sex on children's time in the labour market and in school. The results of table 1 were obtained from regressions run on a 1971 national probability sample of 979 rural Indian households with children; a full report of the study and details of estimation can be found in Rosenzweig (1981). The results indicate that a rise in the value of one person's time significantly affects the time allocation of other family members. In particular, where adult female wage rates were high, both sons and daughters were evidently less likely to be attending school, and daughters, but not sons, were less likely to be employed in the labour market. In contrast, where adult male wage rates were high, for given levels of female and child wages, children were significantly more likely to be attending school and were less likely to be working in the labour market.

Table 1. Matrix of family wage effects on activities of mother, daughters, and sons in rural households, Indiaa

  Labour-force participation Schooling attendance indexc
Mother Daughters Sons Daughters Sons
Log of child's wage

in district

-0.159 0.454 0.748 -0.486 -0.376
(2.31)b (0.92) (1 45) (2.54) (1.84)
Log of mother's

wage (predicted)

0.046 -0.696 0.053 -0.118 -0.375
(0.68) (1.44) (0.10) (0.63) (1 86)
Log of father's

wage (predicted)

-0.184 -0.087 -1.00 0.748 0.929
(3.90) (0.26) (2.82) (5.64) (6.65)

(x 10-2)

-0.203 -0.888 -0.909 0.585 1.64
(1.52) (0.93) (0.90) (1.48) (4.41)

a. For a list of all included variables, estimation procedures, variable construction, and data description see Rosenzweig (1981).
b. Absolute values of t-ratios beneath regression coefficients.
c. Age-standardized index of attendance. Source: NCAER-ARIS.

Table 2. Matrix of family wage and schooling effects on activities of daughters and sons, Philippinesa

  Hours per week in labour market Schooling attendance indexc
Daughters Sons Daughters Sons
Child's wage -0.011
(3 67)b
Mother's schooling


Father's wage -0.004

a. For a list of all included variables, estimation procedures variable construction and data description, see Rosenzweig (1978).
b. Absolute values of t-ratios beneath regression coefficients.
c. Age-standardized. Source: National Demographic Survey 1968.

The matrix of wage-rate effects from Indian data suggest, moreover, that the times of mothers and female children appear to be closer substitutes in the household than those of mothers and male children, but the opposite is true for fathers' time. A to per cent rise in the adult female wage is associated with an 8 per cent fall in daughters' labourmarket participation (rise in home time), with little effect on that of sons; while a similar rise in the adult male wage lowers the market participation of sons (raises non-market time) by 9 per cent, with only a small drop for female children. The results thus suggest that attempts to encourage the employment of adult women in agriculture, where most employment is concentrated in India, would increase the time spent by children, particularly girls, in the home by lowering both their participation in earnings activities (girls) and their time in school (boys). The results also indicate, however, that, symmetrically, increases in employment opportunities for children that result in higher child wage rates lower the labour-market participation rates of their mothers. By increasing the cost of children's time, they also lower children's time in school. The symmetry of cross-child and maternal wage effects on labour supply is an important implication of the economic theory of the household.

Table 2 shows parallel estimates from a 1968 national probability sample of 1,829 Filipino households (rural and urban) containing women aged 35-49 (cf. Rosenzweig, 1978).

Some patterns of cross "wage" effects found in the Indian data are replicated in the Philippines sample, although this study utilized the mother's schooling attainment instead of the mother's wage. First, where adult male wages are high, so are the school attendance rates of children. Second, in families where the mother is more educated, market work by daughters is significantly lower, while that of sons is only marginally affected. Since better-educated Filipino women are more likely to work (Rosenzweig, 1976), this result suggests again that daughters' non-market time may be more substitutable (than sons' would be) for that of mothers. Third, when child wage rates are high, school attendance rates are low. The only significant discrepancy between the Indian and Philippine results is the positive and significant association found in the Philippine data between the mother's schooling attainment and the school attendance rate of the children. This suggests that schooling attainment, in addition to being a correlate of the wage, may also reflect parental preferences for schooling.(4)

The empirical results from India and the Philippines illustrate the importance not only of changes in income level, but also of the means by which these changes take place. Different means of changing income may result in different patterns of household resource allocation. The implications for data collection and data analyses are clear: information should be obtained on the wage rate of every family member who works. Conversely, information on "total family income" is of little value for testing models or for policy evaluation. Estimates of the effects of variations in total family income on whatever measure the researcher and/or policy-maker is interested in are not very useful for two reasons. First, such measures obscure the fact that pure income transfers have different effects from wage rate changes which alter the value of individuals' time. Income transfers and wage rate changes represent two distinct policy levers. Second, variations in total family income reflect intra-household differences in the allocation of time to the market by family members as well as wage rates. Since time allocation is an important variable, subject to family decision-making, variations in total family income will reflect household preferences as well as market returns on work. Estimates of "family" income effects will, therefore, not correspond to true income effects induced by income transfers; they will be contaminated by household preferences. Note that, for the same reasons, the earnings of family members are endogenous variables in the model, since the earnings of any family member i are just WiTiW, where, in (7), Tiw is a choice variable unless work time is constrained in some way. Of course, estimates of all relationships obtained from multivariate analyses employing such endogenous variables as family income and/or earnings as "control variables" or covariates are biased, unless very special conditions are met.

Additional complications arise when some members of households do not participate in the labour market. The value of time of such "non-working" individuals is not then equal to the market wage but is instead a function of all parameters characterizing the household, and is endogenously determined. An increase in income to the household (through transfers, for example) will generally raise the value of the time of all of the household's nonmarket participants (Willis, 1973; Gronau, 1973), leading to reallocations of time and goods. Thus, the consequences of an income increase will not only depend on the source of income but on the extent of labour-market participation by family members. In the exetreme case where no family members work for a constant wage rate, it is then very difficult to predict the consequences of interventions without knowledge of the family objective function (4) and the household technology (1) and (3). Estimation of the fundamental parameters characterizing these essential features of the household is difficult at best, and there have been few attempts to estimate, in particular, household technology parameters. I will discuss issues associated with the estimation of household production relations, as they pertain to intra-household allocation, in the fourth part.

Food Prices, Household Food Consumption, Nutritional Status, and Health

The increased attention governments of many developing countries are paying to the "basic needs" of their populations has motivated a number of econometric investigations into the nutritional consequences of food price variation (Pinstrup-Andersen et al., 1976; Alderman and Timmer, 1980; Pitt, 1983; Strauss, 1983). Many policies adopted by developing countries (tariffs, support prices, ceilings, export taxes) and development agencies (food aid) serve to alter the price structure consumers and food producers face. Knowledge of how changes in food prices affect the distribution of food, the nutritional status, and health of the population is crucial to effective policy-setting. Yet, equations estimating the household expenditure system in these studies utilize foods (sometimes converted into nutrients) aggregated over all household members; they do not estimate the individual-specific food demand or health equations (7). Since the price structure pertaining to goods (foods) is the same for each household member i, as noted, such aggregation is permissible (Hick's Composite Good Theorem), and the usual restrictions of demand theory (symmetry, negative own compensated price effects) apply to the household aggregations. Because no such restrictions hold for the individual-specific health or food consumption reduced forms (7), few inferences can be made from these estimates of aggregate household food demand equations about the effects of changes in food prices on the consumption of individual family members in those households. That is, when aggregate calorie availability in the household goes up, one cannot infer who in the household consumes those calories or whether such calorie consumption is beneficial. Moreover, in the absence of information on the health technology in (1), little can be said from aggregated foodconsumption studies about the impact of food price changes on health. Using such household-level food-demand estimates for establishing policy or for designing interventions may be misleading (cf. Pinstrup-Andersen and Garcia in this volume).

The theoretical ambiguity with respect to the effects of a particular food price change on the level and pattern of nutrient consumption at the household level, arising from theoretically unsigned cross-price effects, is well known. Additional ambiguities arise with respect to the effect of changes in individual food prices on the health status of family members. These are due to a lack of information on how the household distributes food and other resources among its members and on how various foods differentially affect the health of individuals. Consider the simple model in the first section, modified to include more than one food type so that there are aggregate cross-price effects. The reduced form effect of a change in the price of food on the health of individual i, when there are m foods, is given by:

and the effects of a change in food price k on the household's aggregate consumption of each food is given by:

, 1=1 ,.....,m.

Thus, knowledge of the effects of food price changes on household consumption of all foods in (9) cannot be used to predict how that food price, if altered, would affect anyone's health, the magnitude of (8), without the knowledge of how each food Xl affects health (the production function (1) for each individual), and/or of the individual-specific consumption price effects dXil/dpk from (7).

Since reliable data on individual-specific food intakes are expensive to obtain, few surveys have collected this information (cf. Pinstrup-Andersen and Garcia, this volume). More common, and less expensive to obtain, are measures of health for individuals. With the latter, estimates of the health reduced-form equation (7) may be estimated, given suitable price variablity. While such reduced-form estimates do not provide information on how the consumption of food items directly affects health (the health technology), they do yield information on how changes in the prices of foods, medical services, and other goods result in changes in the health or nutritional status of individuals. If that is what policy-makers want to know, then collection of health information for individuals and comprehensive price information is sufficient; collection of such information is surely less costly than is the measurement of a household's complete diet and especially of individual food consumption. While there may be good reasons to want to know how households alter their demand for, say, wheat when commodity prices change, this information is not very useful in predicting how the health status of individuals is affected. Moreover, it is a poor choice of a measure to use in the (health) project identification stage.

In Pitt and Rosenzweig (1985), estimates of food price effects on the aggregate household consumption of foods converted into nine nutrients were obtained and compared to estimates of how variations in the same food prices affected the incidence of illness among heads of households and their wives (all heads were males), based on a probability sample of 2,847 farm households in Indonesia. Table 3 excerpts those findings: the effects of four food prices (out of ten) on the nine nutrients and on individual illness probabilities. Only one of the four food prices is unambiguously and negatively associated with the aggregate consumption of all nutrients in the household. An increase in the price of fruits actually increases the consumption of all nutrients except vitamin C, although an increase in the vegetable price appears to significantly lower nutrient consumption for four nutrients. Alterations in the price of sugar appear not to significantly affect the aggregate household consumption of any one nutrient.

The estimated effects of the food price changes on the illness of individuals in the household, provided in the last two columns of table 3, reveal a very different picture of the importance of those food prices for health status, showing a distribution pattern that could not have been anticipated from the nutrient "availability" findings. First, while a fall in the milk price evidently significantly lowers the consumption of all nutrients, variations in milk prices are unrelated to the actual incidence of illness among either farm heads or their wives; the reductions in nutrient consumption may fall predominantly on other household members. Second, while vegetable prices are significantly and negatively associated with the incidence of illness for the male heads of households, rises in vegetable prices do not appear to increase the incidence of illness for farm wives. This uneven distribution of the health effects of vegetable prices is statistically significant (Pitt and Rosenzweig, 1985). Similarly, increases in the price of fruit appear to raise marginally the incidence of illness for farm wives, but not for male farm heads. This differential is not statistically significant, however. Finally, despite the sugar price exhibiting no statistically significant association with household-level nutrient consumption, higher sugar prices are significantly associated with lower illness probabilities among farm heads, but not among farm wives.

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