Second approach: measuring equity and progressivity of financing

While the first approach to equity analysis evaluates the impact of insurance membership on the expected cost of care, the second and more common approach focuses on the distribution of health care costs in relation to a socioeconomic variable. This approach measures equity in financing based on concentration and Kakwani indices. These indices and the approach are discussed below.

3.4.2.2.1 Measuring inequality in cost of care distribution using concentration index

A concentration curve is the generalised form of the well known Lorenz curve. Technically speaking, the concentration curve is a monotonically increasing cumulative density function showing distribution of the variable of interest sorted by socioeconomic status (Roy, Chakravarty and Laha 1959, Mahalanobis 1960, Wagstaff, van Doorslaer and Paci 1991, Kakwani, Wagstaff and van Doorslaer 1997, Cowell 1995). This distribution is subsequently compared with a uniform distribution that represents equality. In the current study, we evaluate the cumulative proportion of cost of health care plotted against the cumulative proportion of population ranked by consumption expenditure. A concentration index (CI), in turn, measures the departure of the concentration curve from an egalitarian distribution, and is therefore used as a summary measure of socioeconomic inequality in the distribution of health care costs.

Following the notation from O’Donnell et al (2007a), a concentration index (CI) can be represented as twice the area between the concentration curve and the line of equality:

89 = 1 − 2 : ;⁶ _<=>=

? [3.4.2]

where Lh(p) is the cumulative function of cost of health care sorted by socioeconomic status.

The concentration index is best applied to cardinal variables with non-negative values; hence cost of health care is an appropriate candidate. Since CI is invariant to multiplication or division by a constant scalar (Kakwani 1980), choice of the type of currency or its denomination, or a uniform change in the time period of cost incurrence that does not alter the proportional relationship between individuals in terms of relative cost incurrence, the

Chapter 3.4 Review of equity and progressivity indices

68 | P a g e value of concentration index will not change. Also, if the choice of the socioeconomic variable changes from consumption expenditure to total income or wealth, and such change does not alter the rank order of individuals, then the concentration index will remain unchanged.

The value of any CI varies between -1 and +1, with a negative sign suggesting a higher concentration of the cost of health care among the poor [pro-rich], and a positive sign suggests a higher concentration among the rich [pro-poor]. A negative [positive] index can occur in two instances:

1. If the concentration curve always lies above [below] the 45 degrees line, or

2. If the concentration curve crosses the 45 degree line and the area above [below] the 45 degree line is greater than the area below [above].

Similarly, the index would take a value of zero if it lies everywhere on top of the egalitarian line, or if it crosses the line of equality, and the areas above and below the line are equal (Wagstaff 2002a). This can be potentially misleading, and therefore the index should always be studied in conjunction with the concentration curve.

In summary, the sign of index suggests direction of the relationship between cost of health care and the socioeconomic variable, and the magnitude of the index suggests the strength of this relationship (O’Donnell et al 2007a).

3.4.2.2.2 Progressivity in financing and the Kakwani index

Although the concentration index is a useful indicator to measure the degree of socioeconomic inequality in the cost of health care, it does not enable one to say much about progressivity or regressivity of a financing system, defined in relation to the baseline distribution of socioeconomic status. Castano et al (2002) add that a pro-poor pattern of concentration curve may be a delightful finding for an analyst. However if the Lorenz curve for the socioeconomic variable exhibits a pro-rich distribution that outdoes the pro-poor pattern of cost of care, then the true regressive nature of the system will only be revealed when the two distributions are graphically compared.

Chapter 3.4 Review of equity and progressivity indices

69 | P a g e The standard approach used to measure progressivity in health financing involves calculating the Kakwani Index of progressivity (KI). KI compares the concentration index for the cost of care variable with the Gini index, which represents inequality in socioeconomic variables (Kakwani 1977). The Gini index is defined as the area between cumulative distribution of the socioeconomic variable, represented by the Lorenz curve, and the line of equality. Podder (1995) explains that, conceptually, the KI is a measure of elasticity that quantifies proportional change in the cost of care variable in relation to change in socioeconomic status.

Mathematically, the Kakwani index is twice the area between the concentration curve for the cost of care and the Lorenz curve for the socioeconomic variable (equation 3.4.3).

@_A= 2 : B;⁶ _= − ;<=C>=

? [3.4.3]

Here @_A is the Kakwani index, Ly(p) represents the Gini index (G) based on the Lorenz curve, and Lh(p) is the concentration index (CI) based on the concentration curve. Equation 3.4.3 can be simplified as:

@_A = 89_<− D_ [3.4.4]

If the cost of care is progressive [regressive], the concentration curve will lie below [above]

the Lorenz curve, and KI will be positive [negative] (Wagstaff and Doorslaer 2000). The value of the KI ranges from +1 to -2, where +1 represents a scenario when the pre-payment socioeconomic variable is distributed equally among all members of society, but cost of care is borne only by one individual. -2 signifies the other extreme, whereby all of the pre-payment socioeconomic variable is concentrated in the hands of the richest individual, but the entire cost of care is borne by the poorest individual.

In reality, the value of the KI lies between these two extremes. The Kakwani index will be zero if cost of care is perfectly correlated with socioeconomic status, and the two curves lie on top of each other, representing proportionality of financing, or in another case when the concentration curve crosses the Lorenz curve, and the areas above and below the point of crossing cancel out. This makes it important for the KI to be evaluated alongside the graphical representations of the concentration and Lorenz curves (Wagstaff et al 1989).

Chapter 3.4 Review of equity and progressivity indices

70 | P a g e