Table 3: Changes in opportunity-sensitive headcount

|_Countries_|∆_opFGT_0|_population composition efect_|_distribution efect_|_level efect_|
|---|---|---|---|---|
|NL-LT|-0.0716272|-0.0160272|0.0157706|-0.0713705|
|CZ-NL|-0.0231285|-0.0101637|-0.0133965|0.0004316|
|LU-FR|-0.0065687|-0.0200333|0.0181715|-0.0047069|

Source: Authors’ calculation from EU-SILC (2005). Poverty thresholds are defined as the country-specific relative poverty lines in 2004 PPP Euro.

apart by both _FGT_ (0) and _C_ (NL vs. LT); countries ranked differently by the two measures (CZ and NL); and countries ranked similarly by the two indices (FR and LU). The entries listed in the table are the Shapley values for the column effects across all possibly paths of the decomposition given by (6).

Results indicate that differences in opportunity-sensitive poverty arise from different sources in each case. Differences between the Netherlands and Lithuania - ranked at the two extremes of the _FGT_ (0) range in our sample - are unsurprisingly driven by the level effect, with the distribution and population composition effects largely offsetting each other. The Czech Republic is less OS poor than the Netherlands both because the distribution of poverty across types is more favorable, and because poorer types are less populous there. The level effect, as implied by the reverse ranking, goes in the opposite direction. Differences between France and Luxembourg are interesting: although the overall difference in _FGT_ (0) is very small, this actually reflects two relatively large but mutually offsetting effects: The distribution of poverty is more concentrated in poorer types in Luxembourg, but the poorest types are less populous there than in France.

# **7 Conclusion**

The last decade and a half has seen growing interest in inequality of opportunity. A number of different approaches to its formal measurement have been proposed, and applications to both developing and developed countries now abound. From a normative perspective, there is a coalescing consensus that equality of opportunity is the appropriate “currency for egalitarian justice” (Cohen, 1989). From a positive perspective, there is some evidence that inequality of opportunity is more closely (and negatively) associated with future economic performance than inequality of outcomes (Marrero and Rodriguez, 2013).

Yet, although a concern with inequality among the poor has been central to poverty measurement at least since the mid-1970s, sensitivity to inequality of opportunity has hitherto not been introduced into formal poverty measurement (so far as we are aware). This may reflect, at least in part, the fact that measures of inequality of opportunity explicitly depend on personal characteristics other than income, thereby clashing with the standard anonymity axiom. Similarly, most perspectives on inequality of opportunity would treat transfers within and between types differently, requiring adjustments to the transfer axiom.

In this paper, we have sought to address these challenges and to axiomatically derive a class of opportunity-sensitive poverty measures (OSPM). A broad OSPM class was defined, which satisfies the standard axioms of monotonicity, focus and additivity, as well new axioms of within-type anonymity, inequality of opportunity aversion, and (weak) inequality aversion within types. A narrow OSPM subclass was also defined, for the case when weak inequality aversion within types is replaced 17