Putting the cart before the horse. A comment on Wagstaff on inequality measurement in the presence of binary variables

✍ Scribed by Guido Erreygers; Tom Van Ourti

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 64 KB
• Volume: 20
• Category: Article
• ISSN: 1057-9230
• DOI: 10.1002/hec.1754

✦ Synopsis

Adam Wagstaff's (2011) recent paper sends a strong reminder that binary variables occur frequently in health inequality studies and that it is important to examine whether the standard measurement tools can be applied without any modification when the health variable happens to be binary. In his note, he reconsiders what he wrote previously on the subject (Wagstaff, 2005), in the light of recent work on bounded variables (Clarke et al., 2002; Erreygers, 2009a Erreygers, , 2009b;;Wagstaff, 2009;Erreygers and Van Ourti, 2011). Although Wagstaff's contribution undoubtedly enriches a much-needed debate, crucial aspects of his paper seriously misrepresent the positions and views set forth in Erreygers and Van Ourti (2011). In this note, we would like to put the record straight, focusing on five specific points.

1. In Erreygers and Van Ourti (2011), we have tried to make a careful analysis of the issues involved in the measurement of socioeconomic inequality of health/health care/health expenditures by means of rankdependent indices. This paper builds on the extensive literature on the concentration index, to which Adam Wagstaff has made many and distinctive contributions. We pay special attention to the nature of the health variable under consideration, an aspect that in our opinion had been relatively neglected. Because Wagstaff's (2011) recent paper contains a more detailed exploration of the case of binary variables, we welcome it as a valuable input to an ongoing investigation. Unfortunately, its starting point is an erroneous interpretation of our position.

According to Wagstaff (2011), we claim that because binary variables are ordinal, they are ipso facto unsuitable for any inequality analysis. This can only be called a gross distortion of what we maintain in the paper. In fact, after observing that 'ordinal measurement scales do not allow differences between individuals to be compared' (Erreygers and Van Ourti, 2011), we immediately add the following qualification with regard to a variable of a categorical or binary nature: 'If, however, such a variable can be transformed into or proxied by a cardinal variable, it becomes possible to compare these health differences.' (Erreygers and Van Ourti, 2011) It is also instructive to reflect on the footnote that we append to this sentence: 'For example, van Doorslaer and Jones (2003) have projected the ordinal