The Social Welfare Model For Inequity Analysis By Gravelle et al (2006)

Gravelle et al (2006) demonstrated equity in health care and the social welfare by establishing a welfare maximisation model which yields horizontal and vertical equity as a necessary condition for an optimal allocation of health care. The model is based on the following assumptions;

 The model is based on value judgment that the utilisation of health care by individuals matters only because of its effect on individual welfare and general state of health.

 The welfare function is assumed to be additive. The additive nature of the welfare function reflects a judgment that the marginal welfare for each individual from increased utilisation is independent of the level of utilisation or welfare of other individuals in the society.

 The welfare function is also assumed to be neutral between individuals. This implies that each individual's welfare receives the same weight in the welfare function.

 The model also assumes that the values of the coefficients are non negative.

 The model is based on the assumption that the utilisation of health care by individuals affects the individual welfare and the social welfare has the same functional form across the individuals.

The model

Given a simple welfare maximisation model with an objective function;

^{V v(yi,xi,ci)} = ₀⁰ ₁⁰ _{1 2}⁰ _{2 3}^{0 2} 12 )

(  x_i  x _i c_i y_i y_i ………(1) Where V_i is the welfare that accrues to an individual from his/her utilisation of health care, and V_i also represents the health of individual due to the consumption of health care. The independent variable y_i shows the utilisation of health care by individual i and x_i is a vector of individual morbidity and non-morbidity socioeconomic characteristics that affect the social value of health care while ci is the cost of accessing the service which may also depend on the individual‟s characteristics as well as the pattern of supply of health care. The welfare function vi reflects the value judgment that the welfare of individual depends only on their characteristics not their identities, so that two persons with the same yi, xi and ci characteristics generate the same welfare.

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To analyse the welfare model, we assume that the health policy problem is to choose levels of individual utilisation so as to maximise an aggregate welfare function given as;

W V(y_i,x_i,c_i) subject to yiS ………... (2) This represents the policy maker‟s maximisation problem of the aggregate welfare function given the individual level of utilisation which is subject to the constraint that total utilisation of health care of the individual agents cannot exceed the supply of health care resources. Optimal utilisation of health care in the aggregate social welfare function by each individual is depicted by the equality of the society‟s marginal value of utilisation across all individuals. This is represented in equation 3 as;

yi

W



 =

i i

y V



 (S,x,c)= (_^+ i o

i X₁

 +₂ ^X₂ⁱ ₃ ^ci :)^yi ……. (3)

The λ in equation 3 is the langrage multiplier of the welfare maximisation problem which shows the marginal value of utilisation of the welfare optimisation. The λ depends on total supply of health care S, the distribution of individual characteristics x and access costs c. To know the individual utilisation level, we solve for optimal use of health care resources of each individual, which is given as;

*

yi = _ ₁x₁₂x_2i ₃c_i 



S,x,c



+……….(4) _j ⁰_j /,⁰/

xi and ci are characteristics of individual i which affect the amount of health care he/she ought to have as need variables. The optimal consumption is therefore determined by the need characteristics of individuals and via λ on the needs characteristics of all other individuals as well as the total S which is the total supply of available health care. If the optimal consumption of health care is determined by the need characteristic, it means the optimal allocation of the health care resources is characterised by horizontal equity in health care utilisation; that is individual with the same levels of needs received the same treatment or equal share of health care resources in the process of utilisation.

If it is assumed that access cost c affects the marginal welfare from utilisation due to the reason that α3 ≠ 0. Then, individuals with the same need characteristics will receive different treatment, meaning that the optimal allocation implies vertical equity or the appropriately different treatment of those with different needs.

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The differences in utilisation between individuals i and j with different levels of needs variables is given as;

*

* j

i y

y 

=

₁



x_1i:x_1j



₂



x_2i x_2j



₃



c_i c_j

 ………... (5)

Suppose however that the true model of actual rather than optimal utilisation is

yi = ^



^{ }



^



i ji j

j i

ji j

o X c Z e

2

1

3 





 ……….(6)

ei is the random error. The Z_ji are the non–need characteristics of the individuals that affect their consumption of health care but ought not to that is, income, education, gender and ethnicity. If e_i 0it means X_ij are the only needs variables then individuals with the same needs variables receive different amount of care. If_i 0, it means utilisation of health care is affected by non-need variables and this implies horizontal inequity. If _j _j it means utilisations does not vary appropriately with need variables, and this implies vertical inequity. Gravelle et al (2006) conclude that inequity exists when utilisation of health care is determined by non-need variables such as socioeconomic factors.

The social welfare model for equity analysis by Gravelle et al (2006) is a ground breaking model for the analysis of horizontal and vertical equity in health care.

The model gives a comprehensive description of welfare optimisation by policy makers in the utilisation of health care by each member of the society. The model is in line with previous models of welfare by the utilitarian theory given the assumption of additivity, neutrality and same marginal utilisation values. However, these assumptions may not hold in real life as some individuals will not deliberately utilize the services even though they are available due to religion, and other factors such as acceptability, perception, preferences, life style and culture. As such, the marginal value of utilisation will not be equal. This raises the question of responsibility and access issues in determining inequity (unfair inequality) in utilisation of health care services. The direct measure of inequity based on Gravelle et al (2006) model is indicated by differences in utilisation that is based on income and other socioeconomic factors. The model is deficient because, differences in utilisation due to preferences, perceptions, acceptability, life style and other issues of responsibility are not reflected in the model.

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3.2.3.3 The social welfare model for equity by Fleurbaey and Schokkaet (2009)

In document INEQUITY IN MATERNAL AND CHILD HEALTH CARE UTILISATION IN NIGERIA (página 93-96)