## 1. Introduction

Starting with Gini (1914), the literature on economic inequality has proposed a variety of inequality measures and characterized these measures in terms of their normative properties (see Foster, 1985; Kolm, 1999; Chakravarty, 1999; and Cowell, 2000 for surveys). In practice, measures like the Gini or Atkinson indices are widely used in studies comparing income inequality across countries and over time (see, e.g. OECD, 1995). Such studies often employ several measures at a time, which differ in terms of their implied degree of inequality aversion. This pluralistic approach reflects a prevailing uncertainty as to the proper evaluation of income distributions.

The present paper aims to shed some light on this issue. Our maintained hypothesis is that an inequality measure should reflect the evaluation of income inequality by the citizens. The purpose of the paper is to identify this evaluation. Specifically, we seek to estimate the degree and nature of inequality aversion of Europeans. By considering a representative sample of about 60,000 citizens in 10 European countries, 1978–97, the paper identifies those inequality measures (from a given class of measures) which reflect people's evaluation of the distribution of income most accurately. This may inform the selection of inequality measures to be employed in cross-section or time series studies of European income inequality.

Our approach is based on insights from the theoretical and empirical literature on the measurement of social welfare. Using data on reported subjective well-being (SWB) and relating them to income data we estimate a typical European citizen's welfare function over income distributions. In order to make its estimation operational we have to put some structure on the problem: we utilize the fact that social welfare can be decomposed into an efficiency aspect (level of incomes) and a distributional aspect (inequality of incomes). From this (theoretical) perspective, social welfare can be represented as a function of average income and the inequality of the distribution considered. By using the decomposability of welfare and by choosing an inequality measure (from a given class) and some functional form, we are able to establish an (empirical) social welfare function.

This exercise can in principle be done for any inequality measure. Since alternative measures represent different degrees of inequality aversion, the above procedure does not *per se* allow us to identify citizens' inequality aversion. In order to achieve this, we postulate that a proper inequality measure must be representative for the underlying social welfare function. Therefore, it has to be identical with the measure implicitly implied by the estimated social welfare function. Such a measure is called self-consistent with respect to the welfare function to be determined. Self-consistency permits discrimination between various inequality measures. In the empirical welfare function considered, it manifests itself as a relationship between the coefficients on average income and the respective inequality measure. Coefficient estimates therefore allow us to identify those measures that are consistent with people's view of inequality. In addition to self-consistency, as a theoretical requirement, we will request that admissible inequality measures be statistically significant. Having identified these measures, people's inherent inequality aversion can be investigated.

In our analysis we consider the needs-adjusted income distribution and examine its average and inequality. In order to adjust the income distribution for different needs each household is assigned its equivalent income (the living standard of a representative household member) and a weight representing its size. The equivalent income is household income divided by an equivalence scale. As weight we use the number of household members.

Employing SWB as a standard for evaluating income distribution is based on a “neo-utilitarian” view of social welfare (see Kahneman *et al.*, 1997). In this view, SWB is taken as a proxy of individual utility, and the average relationship between SWB and different economic conditions—e.g. inequality—is interpreted as a welfare function on which to base the social evaluation of those conditions (see Kahneman and Sugden, 2005). This approach to applied welfare analysis is increasingly adopted in the economics literature (see Frey and Stutzer, 2002; Bruni and Porta, 2005) and is underlying our empirical investigation. The role of the SWB indicator in this approach is entirely instrumental.

Our paper adds to recent empirical literature using data on SWB to explore the evaluation of income distributions. Alesina *et al.* (2004) provide an econometric study of the relationship between SWB of a large set of survey respondents and the Gini coefficient in several European countries and U.S. states. They find larger regression coefficients in their European than in their U.S. sample, which they take to suggest pronounced differences in the respective degree of inequality aversion.

Unlike that paper we address the efficiency and distributional aspects of welfare *jointly* within a unified theoretical and empirical framework. Furthermore, we systematically examine an entire class of inequality measures (being a generalization of Atkinson and Gini measures). Our framework allows us to identify those measures from the Atkinson and Gini class that are proper representations of an underlying welfare function and to investigate European people's view of inequality and their inequality aversion.

In our empirical analysis we find that the self-consistent inequality measures incorporate strong inequality aversion. The Gini measures which we find to be self-consistent indicate that people's evaluation of income distributions focuses more on lower than on higher incomes. Moreover, we find that, in addition to the level of income, their ranking is an indispensable factor in people's evaluation of income distributions. At a more general level, our findings suggest that European citizens dislike inequality more strongly than is implied by the Gini coefficient (used by Alesina *et al.*, 2004) and other frequently employed measures of inequality. Studies of inequality which use common measures may thus inadequately reflect European citizens' inequality aversion.

The paper is structured as follows. In Section 2 we set up our theoretical framework. In Section 3 we discuss our empirical data and approach, and in Section 4 we present our results. Section 5 concludes.