The distribution of health and income: a theoretical framework

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Abstract

A general framework is developed to analyse variations in the distribution of population health, where individual health is modelled as a function of income, conditional upon the level of another factor such as health-related behaviour. Results are derived for the response of the level of average health in a population and the degree of health inequality to alternative health promotion policies and equiproportionate income growth. Qualitative results are shown to depend on characteristics of the individual health production functions and the frequency distribution of the other factor at each income level. These results are independent of the distribution of income. The discussion focuses on the implications of these results for contemporary research into inequalities in health and income.

Introduction

Study of the determinants of the health of populations and variations in health within them is currently attracting multidisciplinary interest. Individual lifestyles (Kenkel, 1995), genetic factors (Baird, 1994), psychosocial factors (Wilkinson, 1996), material factors (Pritchett and Summers, 1996; Fiscella and Franks, 1997), health in infancy and childhood (Barker and Osmond, 1987) and access to/response to medical care (McCord and Freeman, 1990) have been proposed as influential determinants of the `average' level of health within a population and the degree of inequalities in health between its sub-groups. Traditionally, research has focused on one of the above factors in isolation, and has paid little attention to interactions between them. More recently however, research has considered how the health response of an individual to changes in one health-influencing factor might be conditional upon the levels of another one. For example, Blaxter (1990), using data from the British Health and Lifestyle Survey, found that healthy behaviour has a strong influence on health in `favourable' circumstances (such as higher social class) but little influence in `unfavourable' circumstances. Forster (1997), using data from the same survey, found a strong impact of education on life-span amongst non-smokers but little effect for smokers. Other recent research (Kooiker and Christiansen, 1995; Birch et al., 1997) has also considered such interactions.

This paper presents a general framework to analyse variations in the distribution of population health. The effect of differential individual health production functions on the expected, or population, health function is shown to depend on the nature of these functions and the distribution of health-influencing factors within the population at each income level. In turn, alternative `shapes' of the expected health function have strikingly different implications for features of the distribution of population health. To illustrate the framework the response of health to changes in an individual's income, conditional upon the `healthiness' of an individual's behaviour, is modelled. However, the framework can be applied to derive predictions for any health production functions that differ amongst sub-groups of the population. These sub-groups may be defined by observable characteristics such as schooling (Kenkel, 1991), or unobservable characteristics, such as the rate of time preference (Fuchs, 1982). In general, all that is required for the framework to be applicable is that individual production functions are non-separable in their inputs.

This paper is organised as follows. Section 2presents a theoretical model of the change in an individual's expected health in response to changes in income. Section 3uses this model to obtain population average health and inequality measures. Section 4develops propositions for the effect of health promotion policy and income growth on the average level of population health and inequalities in health. Section 5discusses the implications of these results for research into inequalities in health, considers directions for future research and concludes.

Section snippets

Theoretical model for an individual

Assume that, for a given population of i=1,…,n individuals, an individual's health (H≥0) is a function of the individual's income (I≥0) conditional on the health-related behaviour of the individual. For expositional purposes, assume that an individual's health-related behaviour can be classified as either healthy (denoted `h'), or unhealthy (denoted `u'). Further, assume that the probability (p) of behaving healthily is an increasing function of the individual's income, p=p(I), 0≤p≤1, ∂p(I)/∂I

The distribution of population health and income

To obtain the average health of the population, take a weighted average of the expected health function for income level I over the n individuals that comprise the population. For any income distribution, this is equivalent to:E(H)=Ei[E(H|Ii)],where E(H|Ii) is as defined in Eq. (1). For a continuous income distribution, the mean for a population is:E(H)=0fIE(H|I)dI,where fI is the frequency density function of I and 0 and ∞ are the lower and upper bounds of the income distribution,

The effect of health promotion policies and income growth on population health and inequalities in health

The framework developed in 2 Theoretical model for an individual, 3 The distribution of population health and incomecan be employed usefully by developing results analogous to those used to analyse the distribution and redistribution of income.

Discussion

This paper has presented a general framework to analyse variations in the distribution of population health, where individual health is modelled as a function of income, conditional upon the level of another factor such as health-related behaviour. The resulting expected health function is shown to be dependent on the characteristics of the individual health production functions and their distribution within the population. Qualitative results have been derived for changes in inequalities in

Acknowledgements

The authors particularly wish to thank Peter Lambert for extensive comments. Also Nicholas Contoyannis, Eddy van Doorslaer, Hugh Gravelle, Charles Normand, Trevor Sheldon, Richard Wilkinson, two anonymous referees and comments from participants at the York Seminars in Health Econometrics: Andrew Jones, Rob Manning, Peter Martinsson, David Parkin and John Wildman. All errors remain the full responsibility of the authors.

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