1. health and fitness

Chapter 3
Theoretical Framework, Methodology, Data
Source and Sample Design
3.1.
Introduction
The review of literature identified the research gaps so as to set the objectives. To
conceptualise the issues and to formulate an appropriate theoretical framework, proper
understanding of the theories relevant to this broad area of health, wages and labour supply
linkage is needed. This chapter elaborately discusses the theoretical framework leading to the
econometric models and relevant estimation issues along with the data source. The
requirement of variables indicates the inadequacy of secondary data sources for the present
thesis. Hence, the sample design for a field survey in order to collect primary data is also
discussed in this chapter.
Evidently, health plays a crucial role in determining the labour productivity among poor
section of the society. In India, not only 72.20 percentages of the total population (Census,
2001) lives in the rural areas, but also majority of them are poor. Therefore, the study
focuses on rural India representing majority of the population and a low income economy, as
well. National Sample Survey data (1999-2000) show that share of agricultural employment
into total rural employment in India is 77.5 per cent, where this figure is highest in case of
Madhya Pradesh (86.43 per cent) and lowest in case of Goa (27.3 per cent). This means
agricultural sector constitutes majority of the rural population in India. Hence, this study
focuses on the agricultural households. The theoretical framework for this study is briefly
discussed in section 3.2. The specification of the econometric model is discussed in section
3.3. Section 3.4 describes requirement of data along with its implications for econometric
analysis. Section 3.5 discusses the sample design followed by a summary in section 3.6.
3.2.
Household Production Function Approach
Based on Becker (1965) and Michael and Becker (1973), a number of models have been
developed and applied to examine several issues such as fertility [Ahn (1991, 1992), Birdsall
(1980)], child schooling [Schultz (1988)], time allocation [Gronau (1973, 1977, 1980)], labour
supply [Killingsworth and Heckman (1986)], health [Behrman and Deolalikar (1988)] etc.
The primary focus of this study is on the relationship between, health, labour supply and
wages in the agricultural sector. An agricultural household is comprised of two fundamental
40
units of microeconomic analysis — the household (consumption unit) and the farm
(production unit). When the household is a price taker in all markets, for all commodities
which it both consumes and produces, optimal household production can be determined
independent of leisure and consumption choices (Singh, et al., 1986). Barnum and Squire
(1979) are the first to derive a household model for agricultural sector, incorporating the
own-farm produced and market-purchased commodities as choice variables along with other
choice variables in the utility function. A farm production constraint is also specified along
with the other constraints in the model.
Singh, et al. (1986) derives a common consistent framework to analyse jointly the farm and
household decisions. Strauss (1986), and Pitt and Rosenzweig (1986) modify the household
models to analyse the health decision of household members simultaneously with other
household decisions and farm production decisions. The theoretical model used in the present
study is based on Singh, Squire and Strauss (1986), Strauss (1986) and Pitt and Rosenzweig
(1986).
Production and consumption decisions in a rural farm household are integrated in this
framework. It demands a complex theoretical structure as well as much data for estimation
issues. This model is useful in two ways: first, it provides the elasticities that could not have
been obtained in a framework where production and consumption decisions, i.e., demand
and supply sides of a farm household are separated. Second, differences in the elasticity
estimates may lead to different policy implication than what we infer from the traditional
estimation results.
The utility of the farm household is assumed to depend upon the consumption of on-farm
produced and market-purchased food commodities, health status and leisure of the members
of the household. It is assumed that the household maximises utility where health is
incorporated as one of the element in the utility function. In this approach the family is
assumed to possess utility function which is a function of ―basic commodities‖. It is also
assumed that the household maximises its utility subject to a set of time and income
constraints. The health status of individual is incorporated as a conditioning factor in the
utility function. The current cumulative health status depends upon the past and current
investment in areas such as preventive health care, nutritional in-take, living environment,
etc.
41
The utility function of the household can be written as
U = U (Xa, Xm, L, H)
(1)
Where Xa is the own-farm produced commodity, Xm is the market-purchased commodity, L is
the leisure time of adult members in the household, and H is the health status of adult
members.
The health of the adult male and female household members is assumed to be influenced by
own-farm produced and market-purchased commodities, health inputs, time inputs of the
adult members, and environmental factors given the individual‘s initial health endowment.
The health production function can be written as
Hj = Hj(Xa, Xm, Xz, L; μ)
(2)
Where Xz is the vector of health inputs, which yield no direct utility and μ is a vector of
individual‘s endowment and environmental factors which are beyond the control of the
household but which affect the health status of the household members. It is assumed that
the own-farm produced and market-purchased food commodities and health inputs and
leisure time of adult members increase the health status of the household members.
The farm output production conventionally depends on a set of variable and fixed factors. In
addition to these factors, the human capital of the farm household is assumed to influence
the farm production.
The farm production function for the own-farm produced food commodity can be specified as
Q = Q (B, G, V, F; H, E)
(3)
Where Q is the value of farm output which is the sum of the commodities used for ownconsumption (Xa), and marketable surplus (N), B is the labour input of adult family members,
G is the hired labour inputs, V is the vector of other variable inputs such as fertiliser, seeds,
bullock labour, etc. F is the vector of fixed inputs namely area of land, capital, etc. H is the
health status of adult members of the household and E is the vector of other human capital
variables namely education, extension contact, farming experience, etc. of adult members in
the household. The agricultural output production function is assumed to be riskless. The
prices Pa, Pm, and Pz are assumed to be not affected by actions of the household. It is also
assumed that the family labour and hired labour are perfect substitutes and can be added
directly.
42
Family and hired labour are assumed to have the same effective labour function, but they are
at different points of the function due to the difference in their intakes. Effective labour is
specified with the help of efficiency wages literature (Bliss and Stern, 1978a, 1978b).
Effective labour is conceptualised as the product of labour hours and a function relating
efficiency per hour worked to calorie intake reflected in health status of the individual. In a
simplified manner this can be conceptualised as following:
The effective family labour input days (B E), depend upon the actual family labour input days
(B) and calorie intake or the health status (H) of the adult members, can be specified as
BE = θ (B, H)
(4)
Any change in the actual labour input (labour days) and health status of the individuals are
assumed to increase their effective labour inputs. The efficiency per work hour function is
often hypothesised to have portion that is increasing at an increasing rate followed by a
portion increasing at a decreasing rate (figure 2.1, pp. 20).
The health status of farm family members may be expected to increase the quantity of
healthy days available for work or leisure. The total available healthy days may be used for
own-farm production as labour inputs, for wage work and for leisure.
The time constraint can be written as
B + M + L = T (H)
(5)
Where M is the total wage-work days of adult members of the farm household and T(H) is
the total available healthy days.
Using (5), (4) can be rewritten as
BE = θ [ T(H) - M - L, H]
(6)
The budget constraint of the farm household is
PaXa + PmXm + PzXz = π + ∑ WBE + A
(7)
From (6) and (7), the budget constrained can be rewritten as
PaXa + PmXm + PzXz = π + ∑ W θ [T (H) - M - L, H] + A
(8)
or, PaXa + PmXm + PzXz = Y*
(9)
43
Where Y* is the full income (Becker, 1965). The household is assumed to maximise the utility
function (1) subject to budget constraint (8), which implicitly includes health (2), farm
production (3), and time (6) constraints.
The Lagrangian function can be written as
£ = U = U (Xa, Xm, L, H) - λ [PaXa + PmXm + PzXz – π - ∑ W θ [ T(H) - M - L, H] – A]
(10)
From the first order conditions of optimisation, we get;
δ U (.) / δ Xa + [δ U (.) / δ H] [δH / δ Xa] = λ [Pa - ∑ W{δ θ (.) / δ T (.)} { δ T (.) / δ H} { δH / δ Xa} -∑ W
{ δ θ (.) / δ Hj} { δH / δ Xa}]
= λ [Pa – ∑ W δH / δ Xa [{ δ θ (.) / δ T (.)* δ T (.) / δ H} + {δ θ (.) / δ H}]
(10a)
δ U (.) / δ Xm + [δ U (.) / δ H ] [δH / δ Xm] = λ [Pm - ∑ W {δ θ (.) / δ T (.)} { δ T (.) / δ H} { δH / δ Xm}
- ∑j Wj { δ θ (.) / δ H} { δH / δ Xm}]
= λ [Pm - ∑ W δH / δ Xm [{ δ θ (.) / δ T (.)* δ T (.) / δ H} + {δ θ (.) / δ H}]
(10b)
δ U (.) / δH * δH/δ Xz = λ [Pm - ∑ W {δ θ (.) / δ T (.)} { δ T (.) / δ H} { δH / δ Xz} - ∑ W { δ θ (.) / δ H} { δH/δ Xz}]
= λ [Pz - ∑ W δH / δ Xz [{ δ θ (.) / δ T (.)* δ T (.) / δ H} + {δ θ (.) / δ H}]
(10c)
δ U (.) / δ L + [δ U (.) / δ H ] [δH / δ L]
= λ [ ∑ W δ θ (.) / δ T (.) - ∑Wδθ (.) / δ T (.) * δ T (.) / δ H * δH / δ Lj - ∑ W δ θ (.) / δ H * δH / δ L
= λ ∑ W [δ θ (.) / δ T (.) - δH / δ L [δ θ (.) / δ T (.) * δ T (.) / δ H + δ θ (.) / δ H]]
(10d)
From the above results, the marginal rates of substitution between own produced and market
commodities are equal to their price ratio:
δ U (.)
δ Xa
δ U (.)
δ Xm
= Pa
Pm
On the one hand, it indicates that the utility of the farm households are influenced directly by
the changes in the consumption of own-farm produced commodities and leisure of adult
members of the households, and indirectly through the changes in health status of adult
members. On the other hand, changes in the effective labour time, and total healthy days
available to the farm household members for leisure or work influence income of the
household adult members indirectly.
Again, π is the farm profit, which can be measured as:
Π = Pa Q (B, G, V, F; H, E) – Pg G – Pv V – Pe E
(11)
Where, P is the price of output, Pg is the wages for hired labourers respectively. Pv is the
vector of prices for variable inputs like fertilisers, etc., and Pe is the vector of prices for other
human capitals, such as education, extension programmes, etc.
44
Therefore, from the optimisation exercise, we get;
Pa δQ (.)/δ G = Pg
(12)
Pa δQ (.)/δ V = Pv
(13)
Pa δ Q (.)/δE = Pe
(14)
Equations (12), (13), and (14) show that the household will equate the marginal revenue
products for labour, fertiliser, and other human capitals. The farm labour, fertilisers, health
and other human capital demand can be determined as a function of prices (P g, Pv, and Pe),
the technological parameters of the production function, and the fixed area of land and
quantity of capital. Since, equations (12), (13), and (14) depict the standard conditions for
profit maximisation, it can be concluded that the household‘s production decisions are
consistent with profit maximisation and independent of the household‘s utility function.
Now, maximised value of profit can be put into equation (8) to yield:
PaXa + PmXm + PzXz = Y*
(15)
Where Y* is the value of full income associated with profit-maximising behaviour. The whole
optimisation system works in two ways: first, we maximise profits, and then, the household
maximises utility subject to its full income incorporating the maximised value of profit into it.
The demand equations for the own-farm produced, and market purchased commodities (Xa
and Xm), leisure (L) and health status (H) of the adult male and female members of the
household are derived from the utility maximisation exercise. They are expressed in the
reduced form as:
Xa = fk1 (Pa, Pm, Pz, π, W, A, μ)
Xm = fk2 (Pa, Pm, Pz, π, W, A, μ)
Lj = fk3 (Pa, Pm, Pz, π, W, A, μ)
Hj = fk5 (Pa, Pm, Pz, π, W, A, μ)
(16)
The demand functions are the functions of own-farm produced and market purchased
commodities, health inputs, wage rates of adult male and female members of the household,
farm profit and individual health endowment and health-environmental factors. The labour
supply can be conceptualised as the mirror image of demand for leisure (L) and therefore,
can be expressed (from the first order conditions) as,
M = M (Pa, Pm, Pz, π, W, A, μ)
(17)
The comparative statics for leisure (or its inverse, namely labour supply) can be analysed
using Slutsky decomposition equation specified below:
δM/ δW = δM/ δW
U
+ [ T(H) – L – B] δM/ δY*
(18)
45
The first term of the right side of above equation is the compensated own-wage effect and
the second term is the income effect. The left hand side of the equation is the
uncompensated substitution effect.
Again, change in own-produced food commodity on the health status of the adult members
can be shown as:
dHj = Ha δXa + Hm δXm + Hz δXz + HL δL
dPa
δPa
δPa
δPa
δPz
(19)
The first and second terms on the right hand side are the effects of an own-farm produced
commodity price change on own consumption and marketable goods, third term is the ownproduced goods‘ price effect on health inputs and the last term is the effect of price of own
farm produced good on leisure (or work time).
Now, for consumption commodities (Xa, which is also produced by the household), own price
effects are:
dXa = δXa
dPa δPa
+ δXa δY*
Y* δY* δPa
(20)
The first term on the right hand side is negative for a normal good. The second term captures
the profit effect, which occurs through the increase in the price of own-produce resulting in a
rise in farm profit and thus the full income.
Now, using envelope theorem, we can write,
δY* dPa = δπ dPa = Qa dPa
δPa
δPa
(21)
This implies that the profit effect equals output times the price increases and therefore is
unambiguously positive. This effect can be inferred directly from this model because of the
joint presence of production and consumption decisions.
3.3.
Methodology – Specification and Estimation Issues
The analysis is done using the methods of ―Description‖, ―understanding‖, ―reduction‖ and
―disaggregation‖. The patterns of health, labour productivity, Labour supply and wages are
described on the basis of charts, tables, and shape distribution of each variable.
Understanding is done through the exploration of pattern of variables on the basis of
cartography, statistical tables and econometric models. In addition to that, conventional
measures of two-way association test are used to reduce the relationship between and
among variables. Contingency matrices have also been constructed to disaggregate and thus
grasp the inherent diversity in the relationship between and among variables.
46
As far as econometric model selection is concerned, simultaneous equation approach,
particularly simultaneous equations in the reduced form is found to be appropriate to
estimate the effect of health status on productivity. In addition, the study uses Box-Cox
Double Hurdle Model to estimate burden of income loss due to illness at the household level
for different group of individuals.
The understanding is largely based on the household production function framework, which
combines both the household and farm production decisions. Although these decisions are
simultaneous at a point in time, it can be separable under certain assumptions. For example,
if the household is assumed to be price taker, in the presence of labour and product markets,
all prices in this framework become exogeneous to the household. As a result, the production
decision turns to be independent of labour supply and other household decisions. In this
situation, the demand functions for labour, health, and farm production function can be
estimated separately.
The household labour supply and health are functions of a set of prices and income, shown
as reduced form equations where no simultaneity exists [Sen, 1966; Nakajima, 1969]. In
some literature it has been shown that given the assumptions made about markets, the
household production and consumption decisions can be modeled recursively, even though
they are simultaneous in time (Nakajima, 1969; Jorgenson and Lau, 1969).
Now, if the error terms in the household labour supply and health equations are uncorrelated
with the errors in production function equation, each equation may be estimated separately,
and the single equation method can be used (Singh et. al., 1986). However, if they are
correlated, the model cannot be estimated by single equation method irrespective of its
separability. The endogeneity generated due to correlated errors in the model, must be taken
care of. Under semi-commercial farming as discussed in Singh et al., (1986), there are certain
imperfections in the product and/or agricultural labour markets in developing economies; or
market does not exist at all for certain types of labour or products in agricultural sector. In
the context of India, in majority of the cases, the farms are operated and managed by
individuals/households as self operating enterprises.
There is no labour market for farm
management and operation. This implies that hired labour market cannot be a perfect
substitute for supervision and input-output allocation. On the one hand, knowledge and
experience regarding farming acquired over time results into high skill for a farmer. This skill
cannot be sold or purchased in market, and hence, becomes augmented with the farmer as
human capital. On the other hand, health is also a non tradable basic commodity produced at
the household level. Therefore, in this scenario, household decisions and farm production
decisions may not be separable. This leads to specify health, labour supply and farm
income/profit in a simultaneous equation framework. Thus, taking endogeneity of any choice
47
variable into consideration, a set of structural equations may be estimated (Singh, et.al.,
1986).
The structural equations of the model can be specified tentatively as:
M = α1 + β11H + β12 Ln Q + ∑ β13 Ln W + ∑ β14 A + β15 D1 + β16 D2 + u1
(22)
H = α2 + β21M + β22 Ln Q + ∑ β23 Ln W + ∑ β24 A + β25 D1 + β26 D3 + u2
(23)
Ln Q = α3 + ∑ β31jM + ∑j β32H + β33 D4 + β34 E + u3
(24)
Where M, H and Q are the measures of labour supply, health and farm production,
respectively. D1 is a vector of individual and household level variables like caste, gender, etc.,
D2 is a vector of labour market characteristics, e.g., distance to nearest urban centre,
distance to the market place where the farm output is sold, number of small scale industries,
etc., D3 is a vector of health infrastructure at household and village level, e.g., sources of
drinking water, distance to nearest medical centre, etc., D 4 is a vector of conventional fixed
(such as land) and variable inputs (such as fertilisers, bullock labour, water, etc.) used in
farm production, E is the vector of human capital variables such as education, farming
experience, etc., u1, u2, and u3 are the random error terms and α‘s and β‘s are the
parameters to be estimated. The model will be estimated using appropriate econometric
technique.
3.4.
Data Requirement
The discussions hitherto indicates that the study requires detailed information on both
household and farm activities. The aggregate level data available from National Sample
Survey (NSS), Census of India, National Family and Health Survey (NFHS) are not adequate
for the purpose, since very little information is available on the exogenous determinants of
the household-farm activities.
Measurement of adult health status as discussed in the last chapter is highly debatable. There
is no unique consensus with regard to the perfect measure or proper method for quantifying
health status. In case of adults (in this study, for 15 – 65 years of age groups), at the
individual level four major well accepted indicators are: Adult height, Body Mass Index (BMI),
Activities of Daily Living (ADL), and Self-rated health status. The study uses information on
height, weight, BMI, history of illness and self rated health status to capture the health status
of respondents.
It is clear that variations in labour productivity under certain assumption of neoclassical
economics should be reflected in wages. Hence, at the individual level, the relative
productivity or partial productivity is used to define the labour productivity in the present
study. For non-wage earner farmers, i.e., for family labourers or for cultivators, productivity
can be measured from the estimation of the farm production function. As it is discussed in
48
the last chapter, the impact of nutrition or health on labour productivity has been analysed at
the micro level by estimating either production functions or wage equations. The individual‘s
wages per hour of work are related to health status (H), acquired skills such as education (E),
experience associated with the age (X), and other unobserved forms of human capital
transfers that are proxied by parent education and occupation (PE).

w = w (H; E, X, PE, ε)
(25)
This is a standard earning function in which health is incorporated as an element. We use the
information on farm production, wages earned by the labourers and income for the purpose
of our study.
Data sets available from NSS 60th round, Census of India and other CSO publications are
exploited to understand the macro scenario. Information on the loss of household‘s income
due to illness provided by NSS 60th round unit level data set (schedule no 25.0) is used to
understand the economic impact of illness at the household level in India. But, the study
requires detailed information on both the household and farm activities for which primary
survey is conducted. Therefore, in addition to the secondary source of information, the study
uses data collected from the primary survey as well. The interview schedule is attached as
Appendix 3.1 at the end of the thesis.
3.5.
Sample design
A multi stage sampling is used to select the sample villages. Based on the agro-climatic
conditions, National Sample Survey Organisation divided West Bengal into four regions,
namely ―Himalayan‖, ―Eastern plains‖, ―Central Plains‖ and ―Western Plains‖. Considering the
proximity and feasibility to conduct a primary survey, the backward region namely ―Western
Plains‖ and the developed region namely ―Eastern Plains‖ are selected. From the ―Western
Plains‖ region, one backward district namely ―Bankura‖ and one relatively developed district
namely ―East Midnapore‖ are selected. Similarly, from the ―Eastern Plains‖ one developed
district namely ―Nadia‖ and one comparatively backward district namely ―Birbhum‖ are
selected.
At the second stage, blocks have been selected. Based on the information available in the
Primary Census Abstract 2001, blocks are selected according to the percentages share of
main workers (cultivators plus agricultural labourers) involved in agricultural activities to the
total number of main workers. The blocks which show more than 50 percentages of total
main workers involved in agricultural activities are considered. Thus, at least one block has
been selected from each district.
49
At the third stage, villages are selected. Considering the time and resource constraints,
villages are selected in each of the selected blocks at random. The local labour market
characteristics, such as distance from the main road, distance from the market area,
presence of any factory or cottage industries so and so forth, are kept in mind while selecting
the villages. Given the nature of the field area in terms of employment, the households are
selected at random. This is primarily because most of the households in rural West Bengal
depend largely on agricultural practices. Finally, 676 respondents have been interviewed out
of 350 sample households for this study. The selected villages, blocks and districts have been
shown in the appendix 3.1 (maps 3.1 to 3.7).
3.6. Summary
This chapter makes an attempt to present the household production model extended for an
agricultural household considering health as a crucial element in the utility of the household
members. This model builds the theoretical framework for analysing linkages between health,
labour supply and farm production. It not only draws the reduced form of the structural
equations, but it also identifies the variables and parameters needed for the study. Hence,
the inadequacy of secondary data source has been highlighted. Therefore, the chapter
discusses on the sample design framed to conduct a primary survey in order to collect
detailed information on households, individual attributes related to health, labour supply
decisiosns, wages, so on and so forth along the information on farm production. The sample
villages are shown in the respective maps provided as appendices.
50
Appendix 3.1. Maps of West Bengal and selected blocks highlighting
the selected villages
Map 3.1. Map of West Bengal highlighting the sample districts
Birbhum
Nadia
Bankura
East Midnapore
51
Map 3.2. Block Kotulpur Highlighting Baragaria and Gopalpur (District: Bankura)
Baragaria
Gopalpur
52
Map 3.3. Block Suri-I Highlighting Singur (District: Birbhum)
Singur
53
Map 3.4. Block Mohammadbazar Highlighting Bherapathar and Asenga (District: Birbhum)
Bherapathar
Asenga
54
Map 3.5. Block Ramnagar II Highlighting Kanjia and Bararankua (District: East Midnapore)
Kanjia
Bararankua
55
Map 3.6. Block Chakdah Highlighting Katabelia (District: Nadia)
Katabelia
56
Map 3.7. Block Haringhata Highlighting Basantapur (District: Nadia)
Basantapur
Source: Census 2001 for all the maps from 3.1 to 3.7
57