at the scholarly level. Ideas first developed by philosophers such as Arneson, Dworkin and Cohen, and by economists such as Sen, have been translated into simple, coherent and powerful models by a number of economists since the 1990s. And these models, in turn, have spawned a subsidiary literature on measurement, with a growing number of empirical applications. Some have now gone beyond the measurement of inequality of opportunity and of implications for public finance, and into issues related to poverty and the assessment of economic growth and development.

Yet at another level, there is still a long way to go. Although it is growing in importance, the literature on inequality of opportunity has not yet been fully incorporated into the economics mainstream. Only a minuscule fraction of the applied literature on impact evaluation, for example, examines the effects of policies on the distribution of opportunity.<sup>30</sup> Although policymakers the world over pay lip service to (or, in some cases, genuinely embrace) equal opportunities, it is not clear that much of that discourse has been informed by the literature reviewed above.<sup>31</sup> We close this chapter by highlighting three challenges that, in our view, face this field of normative economics in its quest for greater relevance.

The first is _robustness_ . The sheer number of different approaches to quantifying inequality of opportunity – direct, indirect, ex-ante, ex-post, etc. – is understandable, considering the inherent difficulty in measuring a concept that refers to unobservable sets of possible counterfactuals as well as the novelty of the field. Yet, it is easy to see that it can appear bewildering to potential users. It is perfectly true, for example, that the ex-ante and ex-post approaches to the compensation principle are distinct and valid alternative ways to defining the egalitarian component of E. Op. Nevertheless, if the concept of inequality of opportunity is to appear as more than mere academic arcana to applied social scientists and policymakers, the field would greatly benefit from a few simple unifying principles that provide robust assessments or comparisons – much as Lorenz dominance placed the measurement of income inequality on a much firmer footing in the early 1970s.

The second is _accuracy_ . The empirically dominant approach to measuring I.Op., as highlighted in Section 5, is currently the between-types specification of the ex-ante indirect approach. Yet, despite its simplicity, this approach suffers from a serious practical limitation: it generates only lower-bound estimates, and how far these lower-bound estimates are from the truth is very much an open question. And, to make it worse, it is an open question that is largely driven by the quality and nature of the data (both on advantage and circumstance variables) available in each application. This naturally makes comparisons across different countries problematic and, in our view, is one factor behind some of the critiques that have been levelled against it (see, e.g. Kanbur and Wagstaff, 2014).

> 30 Brunori et al. (2012), Jones et al. (2014), Van de Gaer et al. (2014) are some examples of this small vanguard.

> 31 One exception was the World Bank’s 2006 _World Development Report_ on Equity and Development.

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