International audienceThis paper employs the theory of equality of opportunity, described in Roemer's book (Equality of Opportunity, Harvard University Press, 1998), to compute the extent to which tax-and-transfer regimes in 11 countries equalize opportunities among citizens for income acquisition. Roughly speaking, equality of opportunity for incomes has been achieved in a country when it is the case that the distributions of post-fisc income are the same for different types of citizen, where a citizen's type is defined by the socioeconomic status of his parents. Intuitively, a country will have equalized opportunity if the chances of earning high (or low) income are equal for citizens from all family backgrounds. Of course, pre-fisc income distributions, by type, will not be identical, as long as the educational system does not entirely make up for the disadvantage that children, who come from poor families face, but the tax-and-transfer system can play a role in rectifying that inequality. We include, in our computation, two numbers that summarize the extent to which each country's current fiscal regime achieves equalization of opportunities for income, and the deadweight loss that would be incurred by moving to the regime that does.

This paper studies evidence from Thomson Scientific about the citation process of 3.7 million articles published in the period 1998-2002 in 219 Web of Science categories, or sub-fields. Reference and citation distributions have very different characteristics across sub-fields. However, when analyzed with the Characteristic Scores and Scales technique, which is replication and scale invariant, the shape of these distributions over three broad categories of articles appears strikingly similar. Reference distributions are mildly skewed, but citation distributions with a five-year citation window are highly skewed: the mean is twenty points above the median, while 9-10% of all articles in the upper tail account for about 44% of all citations. The aggregation of sub-fields into disciplines and fields according to several aggregation schemes preserve this feature of citation distributions. It should be noted that when we look into subsets of articles within the lower and upper tails of citation distributions the universality partially breaks down. On the other hand, for 140 of the 219 sub-fields the existence of a power law cannot be rejected. However, contrary to what is generally believed, at the sub-field level the scaling parameter is above 3.5 most of the time, and power laws are relatively small: on average, they represent 2% of all articles and account for 13.5% of all citations. The results of the aggregation into disciplines and fields reveal that power law algebra is a subtle phenomenon.

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We study the problem of normalizing citation impact indicators for differences in citation practices across scientific fields. Normalization of citation impact indicators is usually done based on a field classification system. In practice, the Web of Science journal subject categories are often used for this purpose. However, many of these subject categories have a quite broad scope and are not sufficiently homogeneous in terms of citation practices. As an alternative, we propose to work with algorithmically constructed classification systems. We construct these classification systems by performing a large-scale clustering of publications based on their citation relations. In our analysis, 12 classification systems are constructed, each at a different granularity level. The number of fields in these systems ranges from 390 to 73,205 in granularity levels 1 to 12. This contrasts with the 236 subject categories in the WoS classification system. Based on an investigation of some key characteristics of the 12 classification systems, we argue that working with a few thousand fields may be an optimal choice. We then study the effect of the choice of a classification system on the citation impact of the 500 universities included in the 2013 edition of the CWTS Leiden Ranking. We consider both the MNCS and the PP top 10% indicator. Globally, for all the universities taken together citation impact indicators generally turn out to be relatively insensitive to the choice of a classification system. Nevertheless, for individual universities, we sometimes observe substantial differences between indicators normalized based on the journal subject categories and indicators normalized based on an appropriately chosen algorithmically constructed classification system. Acknowledgements. This is the second version of a Working Paper of the same title that appeared in this series in March 2014. This paper was conceived while Ruiz-Castillo enjoyed the hospitality of the Centre for Science and Technology Studies, Leiden University, The Netherlands, during the 2013 spring term. RuizCastillo also acknowledges financial help from the Spanish MEC through grant ECO2011-29762. 2

This paper has two aims: (i) to introduce a novel method for measuring which part of overall citation inequality can be attributed to differences in citation practices across scientific fields, and (ii) to implement an empirical strategy for making meaningful comparisons between the number of citations received by articles in 22 broad fields. The number of citations received by any article is seen as a function of the article’s scientific influence, and the field to which it belongs. A key assumption is that articles in the same quantile of any field citation distribution have the same degree of citation impact in their respective field. Using a dataset of 4.4 million articles published in 1998–2003 with a five-year citation window, we estimate that differences in citation practices between the 22 fields account for 14% of overall citation inequality. Our empirical strategy is based on the strong similarities found in the behavior of citation distributions. We obtain three main results. Firstly, we estimate a set of average-based indicators, called exchange rates, to express the citations received by any article in a large interval in terms of the citations received in a reference situation. Secondly, using our exchange rates as normalization factors of the raw citation data reduces the effect of differences in citation practices to, approximately, 2% of overall citation inequality in the normalized citation distributions. Thirdly, we provide an empirical explanation of why the usual normalization procedure based on the fields’ mean citation rates is found to be equally successful.