.mw-parser-output .hidden-begin{box-sizing:border-box;width:100%;padding:5px;border:none;font-size:95%}.mw-parser-output .hidden-title{font-weight:bold;line-height:1.6;text-align:left}.mw-parser-output .hidden-content{text-align:left}You can help expand this article with text translated from the corresponding article in German. (April 2014) Click [show] for important translation instructions. View a machine-translated version of the German article. Machine translation, like DeepL or Google Translate, is a useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text into the English Wikipedia. Consider adding a topic to this template: there are already 8,953 articles in the main category, and specifying|topic= will aid in categorization. Do not translate text that appears unreliable or low-quality. If possible, verify the text with references provided in the foreign-language article. You must provide copyright attribution in the edit summary accompanying your translation by providing an interlanguage link to the source of your translation. A model attribution edit summary is Content in this edit is translated from the existing German Wikipedia article at [[:de:Kakwani-Index]]; see its history for attribution. You should also add the template ((Translated|de|Kakwani-Index)) to the talk page. For more guidance, see Wikipedia:Translation.

The Kakwani index is a measure of the progressivity of a social intervention, and is used by social scientists, statisticians, and economists. It is named after the economist who first proposed and used it, Nanak Chand Kakwani.^[1]

The Kakwani index uses the Gini framework to measure how progressive a social intervention is. It is equal to the difference between the Gini index for the social intervention, and the Gini index for incomes before imposition of the policy intervention. Theoretically, the Kakwani index can vary between −1 and 1; the larger the index is, the more progressive is the social intervention.^[2]

The index is calculated using the following formula:

K_{t}=2\sum _{k=1}^{n}{\frac {1}{n))({\frac {k}{n))-\sum _{i=1}^{k}\gamma _{i})-G_{beforetax},

where $i=1,...,k$ denotes individual $i$ , $n$ is the total number of individuals in society, ${\displaystyle \gamma _{i))$ is the share of total taxes paid by individual $i$ , and ${\displaystyle G_{beforetax))$ is the before-tax Gini coefficient. Using the formula for the Gini coefficient, the equation for the Kakwani index can be reduced to:

K_{t}={\frac {2}{n))\sum _{k=1}^{n}(\sum _{i=1}^{k}\alpha _{i}-\gamma _{i}),

where ${\displaystyle \alpha _{i))$ denotes the share of income received by individual $i$ .

The Kakwani index was originally devised to measure the progressivity of tax systems, in which case, it would be equal to the Gini concentration index^{[clarification needed]} for the taxes collected minus the Gini index for pre-tax incomes.^[2] This can be shown to be equal to the absolute decline in the Gini index for incomes, caused by the imposition of taxation, divided by the average net rate of taxes.^[3]

The Kakwani index is also commonly used to examine the equity of government health care provision. In that situation, the Kakwani index would be equal to the difference between the Gini coefficient for incomes and the Gini concentration index for out‐of‐pocket health care payments.^[1]

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