This analysis draws upon the household production model (Becker 1965) in which households are assumed to maximize their utility function subject to a budget and a time constraint. In line with the theory, households purchase different goods and combine them into a household production system to produce various goods and services under a given time constraint. These purchased goods and produced commodities directly enter into the household’s utility function. Since most human capital outcomes are not available in the market, households have to produce them on their own based on the integration of biological, demographic, and economic considerations.
Consider a one-period household production model with constrained maximization of a joint utility function,31 that is, non-separable determination of household production—consumption decision. Extending the exposition set out in Behrman and Deolalikar (1988), assume that the household preferences constituting of T individuals are represented by the following preference function:
U = U(𝑋𝑖, 𝐶𝑖, 𝑇
𝑙𝑖, 𝐻𝑖)𝑖 = 1, … , 𝑇 (5.1) where 𝑋𝑖 is the consumption of purchased goods of household member i,𝐶𝑖 is the consumption of own production of household member i,𝑇𝑙𝑖 is the leisure time of household member i,𝐻𝑖 is the health of household member i. The utility is assumed to depend on the consumption of goods (both markets purchased goods and own produced agricultural goods), the leisure time and the health status of each of the household members.
The preference function in equation (5.1) is maximized subject to the following constraints. The first constraint is a health production function. The health of the ith individual is produced by the consumption of goods and leisure. Health also depends on the consumption of non-food health inputs which do not provide utility directly (such as medical treatment from local clinics); a vector of household resources (such as drinking water and sanitation facilities); a vector of irrigation
31 The assumption of “unitary” household preference approach may be questioned, but it is still unclear how a cooperative bargaining process affects our outcome variable and changes the theoretical pathways through which improved WATSAN affects health (for further discussion see Alderman et al. 1995; Mwabu 2007).
86
water characteristics (such as types of irrigation water, distance from the household); the i’s innate health endowment and specific individual characteristics, and a vector of community characteristics that include variables that affect an individual’s health (such as access to health facilities, infrastructure and prices, cleanness of the environment).
Irrigation technology can improve health and nutrition by providing nutrient rich and fresh vegetables. It can also improve health by providing greater water availability for domestic use and enables households to maintain key hygiene and sanitation practices (van der Hoek et al. 2002). However, irrigation intervention can affect health negatively in areas prone to vector- borne diseases (Amacher et al. 2004; Ersado 2005).
The health production function then is given by:
𝐻𝑖 = H(𝑋𝑖, 𝐶𝑖, 𝑍𝑖, 𝑇
𝑙𝑖, 𝑇ℎ𝑖, 𝐺, 𝐷, 𝜂𝑖, Ω) (5.2) where 𝑍𝑖 is the consumption of non-food health inputs of household member i (e.g. health care services), 𝑇ℎ𝑖 the time spent on production of health (e.g. taking care of ill family members), 𝐺 a vector of household resources which affect health (e.g. water & sanitation facilities), 𝐷 a vector of irrigation water characteristics (e.g. its type and distance from the dwelling unit where the individual lives), 𝜂𝑖 the observed and unobserved individual characteristics, and Ω the endowment of the households and community characteristics (e.g. the general environment), and the other variables are defined above.
The production/consumption of water for domestic use depends upon the quality of the water source, the time spent by the ith household member collecting water and is assumed to be a function of distance to the water source; the knowledge of good health practices in the household as they relate to water collection and storage, the capital goods used in the transport and storage of water.32 Water quality at the source and quality of water at the POU may substantially vary. The average water quality at the POU can be lower relative to the quality of water at the source as it is affected by factors such as transportation, knowledge of safe water handling, the quality of storage containers and duration time (for a discussion see Wright et al. 2004; Zwane & Kremer 2007).
The second constraint is a water production function that can be defined as follows:
𝑊ℎ = W(ϖ, 𝑇
𝑤𝑖(𝐷𝑤), 𝐴𝑤, 𝐻𝑖, 𝐷, Ω) (5.3)
where ϖ is the quality of water available to the household member i, 𝑇𝑤𝑖 the time spend by household member i on water collection, 𝐷𝑤 the distance to water source, 𝐴𝑤 the capital goods
32 It is possible that and D
w become a choice variable if households can choose among different sources of water for domestic consumption.
87
used in the transport and storage of water (e.g. buckets and pots), and the other variables are defined above.
The household farm production depends not only on the characteristics of all individuals in the household who work on these activities but also on the amount of land, the levels of input use and the practice of irrigation technology. A study by von Braun et al. (1989) shows that utilization of irrigation technology in the production of rice in Gambia increases not only the household’s real income but also it increases their calorie consumption and food expenditure. Agricultural production can also be affected by the household members’ health status either through its effect on the quality of own labor or through reducing labor availability.
The third constraint is a farm production function:
𝑌ℎ = Y(𝐶𝑖, 𝑇
𝑓𝑖, 𝐿ℎ, 𝐴, 𝐾, 𝐻𝑖, 𝐷, Ω) (5.4)
where 𝑌ℎ is the household farm output aggregated overall crops and vegetables, 𝑇𝑓𝑖 the time of the ith household member spent on household farm production, 𝐿
ℎ the amount of hired labor used in farm production, 𝐴 the amount of land used in the farm production process, part of which may be owned by the households (Ah) and the rest of which may be rented (A*), 𝐾 other variable inputs used in farm production and all other variables have been defined above.
Finally, there are time and full-income constraints. Household’s total labor time (T) available is allocated to leisure, health-care activities, water collection, and agricultural production and off- farm income generation:
T = 𝑇𝑙𝑖 + 𝑇ℎ𝑖 + 𝑇𝑤𝑖 + 𝑇
𝑓𝑖 + 𝑇𝑜𝑓𝑓𝑖 )∀𝑖 (5.5) Continuing with the description of the model, it is also assumed that households face a monetary budget constraint where income equals expenditure for consumption goods, leisure, health-care services, expenditure for water container, hired labor is represented by a full-time income constraint as:
𝑃𝑦𝑌ℎ+ R = rA + 𝑃𝑘𝐾 + 𝜔𝐿ℎ+ 𝑃𝑥𝑋 + 𝑃𝑐𝐶 + 𝑃𝑧𝑍 + 𝑃𝑤𝑊 + ∑ 𝜔(𝑇𝑖− 𝑇
𝑙𝑖 − 𝑇ℎ𝑖 − 𝑇𝑤𝑖 − 𝑇𝑓𝑖 − 𝑇𝑜𝑓𝑓𝑖 )
(5.6)
where r is the rental rate of land, R other exogenous income, 𝜔 the market wage rate, 𝑇𝑖 total time of the ith individual, 𝑇
𝑜𝑓𝑓𝑖 the labor market work time of the ith individual, 𝑃𝑗 refers to the different prices, where j = y, k, x, c, z and w.
Maximizing equation (5.1) subject to the (5.2), (5.3), (5.4) and (5.6) constraints yields the following reduced-form demand function for all choice variables in which all exogenous variables
88
appear on the right-hand side of each equation, and the left-hand-side variables are the endogenous variables in the system for the household. Therefore, the reduced-form demand functions for our choice variables are given as:
𝑉 = 𝑓(𝐸) (5.7)
where 𝑉 = (𝐻𝑖, 𝑊ℎ, 𝑍𝑖, 𝑌ℎ, 𝑋𝑖, 𝐶𝑖, 𝑇𝑗𝑖)𝑤ℎ𝑒𝑟𝑒𝑗 = 𝑙, ℎ, 𝑤, 𝑓, 𝑜𝑓𝑓; and 𝐸 = (𝑟, 𝑃𝑠, 𝜔, 𝐺, 𝐷𝑤, 𝑅, 𝐷, 𝜂𝑖, Ω)𝑤ℎ𝑒𝑟𝑒𝑠 = 𝑎, 𝑐, 𝑤, 𝑥, 𝑦, 𝑧
This theoretical framework tries to show the nexus among WATSAN, irrigation and health functions. This framework helps us to identify some policy variables that affect the demand for health, water, sanitation and agricultural irrigation system. Therefore, estimation of the reduced- form demand functions provides a consistent framework.
5.4 Data and Empirical Strategy