On ordinal approaches to the measurement of inequality in well-being, with an empirical illustration based on Mexican data.

Berenger, Valerie (1); Deutsch, Joseph (2); SILBER, Jacques (2) (2016). 'On ordinal approaches to the measurement of inequality in well-being, with an empirical illustration based on Mexican data.' Paper presented at the annual conference of the HDCA, Tokyo 2016.

Most of the literature on inequality in well-being takes a cardinal approach to the measurement of such inequality. When looking at health inequality most researchers have however preferred to take an ordinal view, given the ordinal nature of most data on health status. Several indices have been proposed and they all rely on ordinal data. The purpose of the present paper is to suggest that a similar approach to that which has become common in the literature on health inequality may be adopted when measuring inequality in well-being. The basic idea is that there is some order in which individual accumulate wealth and increase their well-being, whether one looks at the order of acquisition of durable goods or/and that of the services to which the individual or household has access.
In this paper we propose four ways of deriving such an order when the variables under scrutiny are all dichotomous. Such an order will be based respectively on the methodologies of Item Response Theory and Correspondence Analysis, on the concept of “Order of Acquisition of Durable Goods” and on the information relative to the relative frequency in the population of the ownership of durable goods or access to services.
Using these four approaches, we are able in each case to locate the individual/household on the wealth scale corresponding to the order derived and then to compute the cumulative frequencies indicating which percentage of the population has a level of wealth or well-being at least as high as that corresponding to a given stage in the order derived. On the basis of these cumulative frequencies we can finally easily compute one of the measures of ordinal inequality which have been proposed in the literature on health inequality.
Our approach to measuring inequality in wealth or well-being has the advantage of not requiring giving a weight to the various domains of well-being or components of wealth. Moreover the empirical analysis we implemented at the level of the various states of Mexico showed that there was a high degree of similarity between the orders derived from the four different approaches. But it also indicated quite important differences between the Mexican states in the level of inequality in well-being. 

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