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Erschienen in: Social Indicators Research 1/2019

11.08.2018

Inequality and Welfare in Quality of Life Among OECD Countries: Non-parametric Treatment of Ordinal Data

verfasst von: Martyna Kobus, Olga Półchłopek, Gaston Yalonetzky

Erschienen in: Social Indicators Research | Ausgabe 1/2019

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Abstract

The last few years have witnessed an increasing emphasis on going beyond GDP per capita when measuring a nation’s quality of life. Countries (e.g. UK, France, Canada, Germany, Italy, Japan, Korea, Spain) and international organizations (e.g. OECD) have been developing methods suitable for non-income indicators. However, this involves serious measurement challenges due to: (a) multidimensionality, and (b) ordinality (i.e. unlike income these indicators do not have a natural scale). This paper is the first summary of the methods developed in the last decade in the field of inequality and welfare measurement to address these challenges. Next, we utilize the presented methodology and provide evidence on the ranking of OECD countries in terms of welfare and inequality in education and happiness. We find that when dimensions are analysed separately, welfare dominance is frequent (42% of all comparisons in education and 31% in life satisfaction). The number drops to only 4.4% for bivariate dominance, which highlights the empirical relevance of multidimensional analysis. Greece, Portugal and Hungary feature the lowest joint welfare. Northern European countries are most often dominating and Southern European countries are most often dominated in both inequality and welfare analyses.

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2
More precisely, we refer to data that are ordinal and discrete. By ordinal we mean total orders as opposed to cardinality, where numbers are meaningful. Discrete means that there is a fixed number of values, each carries a probability mass as opposed to continuous variables which accord a particular value with probability zero. In general, we can have variables that are: ordinal and discrete (such as health status); ordinal and continuous (such as the Body Mass Index (BMI) which, as the ratio of two continuous variables, is continuous but the differences between two BMI’s are meaningful only in an ordinal sense); cardinal and discrete (e.g. the distribution of the number of cars in households, where there is a fixed number of values, and particular values are meaningful); cardinal and continuous (e.g. income).
 
3
These theories often build upon statistics literature on ordinal data e.g. Blair and Lacy (2000), Berry and Mielke (1992).
 
4
Recent theoretical advances to deal with ordinality are, however, broader and include also poverty measurement (Bennett and Hatzimasoura 2011; Yalonetzky 2012), dissimilarity (Andreoli and Zoli 2014), segregation (Cuhadaroglu 2013), inequality of opportunity (Silber and Yalonetzky 2011), estimation of achievement gaps (Nielsen 2015), etc.
 
5
In Sect. 2.2 we offer a brief discussion on whether bi-polarisation criterion such as AF is an appropriate inequality dominance condition. For more detailed discussion, we refer readers to Kobus (2015). Unarguably, AF approach has been so far the most widely used approach to measuring inequality in ordinal data.
 
6
We thank Professor Brice Magdalou for referencing this work to us.
 
7
We calculated the Gini index by assuming there are two men in each health category, three women in the first health category, two women in the second health category and so on. This is valid since the Gini index is replication invariant.
 
8
We define the median category slightly differently than Allison and Foster (2004) to avoid dealing with multiple medians due to empty categories. Kobus (2015) extends the AF relation to a setting with multiple medians, so in fact \(AF_{\alpha }\) can be extended too in order to allow for multiple quantiles, however this is mostly technical.
 
9
These are large tables of comparisons of each country against each other. They are available on demand.
 
10
An individual enjoys a maximum status if everyone else is either in categories below hers or in her same category.
 
11
We can also visualise the unidirectional relationship between FSD and Definition 6 by noting that: \(H^{+}_{f^s}(i)=H^{+}_{F^s}(i) =\sum _{k=1}^{i-1}2^{i-k-1}F^s_k + F^s_i\). Hence FSD implies Definition 6, but the reverse is not true.
 
12
Obviously, causality may run in both directions, therefore the use of the word “hypothesis”.
 
13
For the actual formula of the standard errors of this section’s statistics see Yalonetzky (2013).
 
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Metadaten
Titel
Inequality and Welfare in Quality of Life Among OECD Countries: Non-parametric Treatment of Ordinal Data
verfasst von
Martyna Kobus
Olga Półchłopek
Gaston Yalonetzky
Publikationsdatum
11.08.2018
Verlag
Springer Netherlands
Erschienen in
Social Indicators Research / Ausgabe 1/2019
Print ISSN: 0303-8300
Elektronische ISSN: 1573-0921
DOI
https://doi.org/10.1007/s11205-018-1962-8

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