Reynolds-Smolensky

Concept

Theoretically, the Reynolds?Smolensky Index is a measure of vertical equity that quantifies the redistributive effect of a tax or transfer system on the distribution of income or other welfare measures. It represents the reduction in inequality attributable to redistribution by comparing inequality before and after fiscal intervention. In health economics, the index is frequently applied to evaluate the equity impact of healthcare financing systems, taxation policies, insurance contributions and public health expenditure.

Mathematically, the Reynolds?Smolensky Index is defined as the difference between the pre-intervention and post-intervention Gini coefficients. The index measures the extent to which redistribution reduces overall inequality after allowing for the effects of taxes, transfers or healthcare financing arrangements. A larger positive value indicates greater redistribution towards equity, whereas a value of zero indicates no redistributive effect.

In practice, the Reynolds?Smolensky Index is estimated using household survey data, income or consumption distributions, and observed taxes or transfers. Pre- and post-intervention Gini coefficients are calculated using standard inequality estimation methods, and their difference provides the index. In health economics, it is commonly used to evaluate the redistributive consequences of health financing reforms and universal health coverage policies.

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Purpose

Used to quantify the redistributive effect of taxation, transfers or healthcare financing by measuring the reduction in inequality achieved through public policy.

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Mathematical Formulae

Primary Formula

RS = G?pre? ? G?post?

where:

• RS = Reynolds?Smolensky Index
• G?pre? = Gini coefficient before redistribution
• G?post? = Gini coefficient after redistribution

Supporting Formulae

None.

Related Mathematical Methods

• Gini Coefficient
• Concentration Curve Analysis
• Lorenz Curve
• Kakwani Index
• Progressivity Analysis
• Distributional Analysis

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Example

A country has a pre-tax household income Gini coefficient of 0.42. After taxes and publicly financed healthcare transfers, the post-intervention Gini coefficient is 0.36.

RS = 0.42 ? 0.36 = 0.06

The healthcare financing system therefore reduces measured income inequality by 0.06 Gini points, indicating a positive redistributive effect.

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Excel Implementation

Function	Example Formula	Health Economics Application
Subtraction	=B2-C2	Calculates the Reynolds?Smolensky Index from pre- and post-intervention Gini coefficients.
IF	=IF(B2>C2,B2-C2,0)	Prevents negative values when assessing expected redistribution.
AVERAGE	=AVERAGE(D2:D101)	Estimates the average redistributive effect across regions or years.

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VBA (Optional)

A VBA macro can automate calculation of Reynolds?Smolensky Indices across multiple healthcare financing scenarios and generate comparative equity reports.

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Sources

• Reynolds, M., & Smolensky, E. (1977). Public Expenditures, Taxes, and the Distribution of Income: The United States, 1950, 1961, 1970. Academic Press.
• Lambert, P. J. (2001). The Distribution and Redistribution of Income. Manchester University Press.
• O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data. World Bank.
• Wagstaff A, van Doorslaer E. Equity in health care finance and delivery.
• Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.