Doing Rawls justice: Evidence from the PSID

Distributive value judgments based on the 'origins' of economic inequalities (e.g. circumstances and responsible choices) are increasingly evoked to argue that 'the worst form of inequality is to try to make unequal things equal'. However, one may reasonably agree that distributive value judgments should also account for the 'consequences' of economic inequalities in such a way as to (i) improve economic efficiency and (ii) prevent from subordination, exploitation and humiliation. In this way of thinking, by resorting the well-known Rawlsian 'fair equality of opportunity' and 'difference principle', the author proposes a pragmatical non-parametric estimation strategy to compare income distributions in terms of Rawlsian inequity and its contribution to overall inequality. The latter methodology is applied to PSID data from 1999 to 2013 and compared with existing empirical evidences on Roemer’s (A Pragmatic Theory of Responsibility for the Egalitarian Planner, 1993, and Equality of Opportunity, 1998) inequality of opportunity. Remarkably, Rawlsian inequity is found between 56% and 65% of the overall income inequality, with an increasing pattern originating from the recent economic crisis. JEL D63 I32 D3


Introduction
"Conservative egalitarians have a dream. They dream of a society in which at some age all individuals have equal opportunities, and in which all inequalities in outcomes can be traced to responsible choices ... there is nothing in this picture which precludes the coexistence of misery and outrageous wealth ... All egalitarians do not have to share this dream, and one can rightly view it as a nightmare. [T]he bulk of the egalitarian program is precisely to fight against this view of social life, and to look for institutions that would enable the population to form a community in which values of solidarity and mutual care would be embodied in institutions and would guarantee that every individual ... would be preserved from subordination, exploitation, humilation" (Fleurbaey 2001, p. 526).
From the perspective of a conservative egalitarian, inequalities are illegitimate (and so, compensation deserving) or legitimate (and so, not compensation deserving) depending on their determinants (e.g., luck, responsible choices), or let's say, origins. This view can be seen as innervating Sen's (1992) capability approach, as well as Roemer's (1993Roemer's ( , 1998 ideal of leveling the playing field, or luck egalitarianism (e.g., Dworkin 1981a, 1981b, Cohen 1989, and strict egalitarianism of opportunity (Arneson 1999).
Differently, outcome egalitarians deny that members of a society are ever non-identical in a distributively important sense. Here, it is said, in the name of individual responsibility and meritocracy, human rights of equal respect, equal social status and participation in democratic arenas are often violated in such a way as to welcome oppression and destitution (Anderson 1999). In this view, inequalities are said to be illegitimate due to their immediate consequences -e.g., subordination, exploitation and humilation -whatever their origins. To the extent that one or the other perspective -origins, or consequences -is spoused, any attempt to reconcile distributive judgments is deemed to fail.
In this paper, we propose a more general approach by which any pairwise disparity is said to be legitimate or illegitimate depending on both origins and consequences of inequality. In this line of thought, we suggest that Rawls' approachbased on the "Fair Equality of Opportunity" and the "Difference Principle" -is a better stepping for both (i) the identification of legitimate social and economic inequalities, and (ii) the measurement of distributive justice (equity).
The contribution of this paper intends to be both methodological and empirical. From a methodological point of view, we propose a 'pragmatical' approach by which inequity -Rawlsian in spirit -can be (non-parametrically) estimated from income distributions. In this scenario, any pairwise disparity is said to be legitimate if it is (i) "attached to offices and positions open to all under conditions of fair equality of opportunity", and (ii) "to the greatest benefit of the least-advantaged members of society" (Rawls 2001). As such, Rawls' meritocracy is defined in a broader setting where both (i) fairness of inequality origins, and (ii) goodness of inequality consequences for the society as a whole, are simultaneously accounted for.
From an empirical point of view, given the separation between social and natural circumstances that is innervating Rawls' thought (Sugden 1993), US income distributions from 1999 to 2013 are compared over time in terms of both Rawlsian inequity and its contribution to overall inequality. Given the PSID resources (Panel Study of Income Dynamics), 64 subgroups are generated from the combination of two binary social circumstances (i.e., place of origin and economic situation of parents in the early years) and four binary natural circumstances (i.e., gender, health status in the early years, ethnicity, IQ-score). Iniquitous income disparities are found to account for 55.7-64.9% of overall outcome inequality. As compared to the 15-20% of iniquitous income disparities as estimated for Roemer's inequality of opportunity (Pistolesi 2009, Abatemarco 2015, our analysis highlights that opting for the Rawlsian idea of justice more than doubles the share of illegitimate inequalities in the US. The paper is organized as follows. The Rawlsian approach to distributive justice is discussed in Section 2. Here, the main rationales and implications of the Fair Equality of Opportunity and the Difference Principle are interpreted according to the main literature. In Section 3, formal definitions are given by which legitimate pairwise inequalities are identified. As a result, an index for the measurement of Rawlsian inequity and its contribution to overall inequality is proposed. Remarkably, we show that Rawlsian perfect equity is attained if and only if (i) all individuals have access to the same investment opportunities in terms of both physical and human capital, (ii) equally responsible individuals achieve the same economic outcome, and (iii) poverty is eradicated from the society. In Section 4, our proposal for the non-parametric estimation of Rawlsian inequity is applied to US income distributions from 1999 to 2013. Section 5 concludes.

Rawlsian Equity
Following the old tradition of 'social contract theory' -whose best known proponents are Hobbes, Locke and Rousseau - Rawls (1971) proposed a normative framework inspired by the ideal of social cooperation for the constitution of a well-ordered society where the stability of political institutions is achieved through the legitimation of social and economic inequalities (reciprocity principle).
Rawls' proposal is grounded on two basic value judgments which are known as the Liberty and the Equality principle. According to the former, "Each person is to have an equal right to the most extensive total system of equal basic liberties compatible with a similar system of liberty for all". This is indicated by Rawls as the principle having priority over the second one which is the one we focus on in what follows.
The Equality principle consists of two ethical value judgments for the identification of fair/good social and economic inequalities within an equity perspective: Fair Equality of Opportunity (hereafter, FEO) and Difference Principle (hereafter, DP). By FEO, social and economic inequalities "are to be attached to offices and positions open to all under conditions of fair equality of opportunity", whereas, by DP, these inequalities are additionally required "to be to the greatest benefit of the least-advantaged members of society" (Rawls 2001).
The former principle (FEO) establishes a norm with respect to the origins of inequality, meanwhile the latter requirement (DP) concerns the consequences of inequality. In this sense, FEO is a condition sine qua non ensuring fairness of existing inequalities, while DP implements Rawls' idea of meritocracy by which goodness, intended as a capacity to benefit the society (especially the least-advantaged), is also required because "the right and the good are complementary" (Rawls 2001).
Remarkably, to the extent that goodness -in addition to fairness -is evoked for the legitimation of inequalities, Rawlsian equity implicitly embodies efficiency issues in such a way as to jeopardize its accommodation in the standard welfare economic theory (e.g., Rawlsian maximin principle is often reformulated in terms of Sen's leximin principle to preserve consistency with strong Pareto efficiency). Furthermore, for the same reason the Rawlsian theory of justice goes well beyond the basic foundations of egalitarianism of opportunity.
In what follows, we recall the basic foundations of both FEO and DP separately, the main objective being the identification of criteria by which a separating line is drawn between legitimate and illegitimate (pairwise) outcome inequalities according to our interpretation of Rawls' theory. 1

Fair Equality of Opportunity
According to Westen (1985), equality of opportunity is a three-way relationship between a person, some obstacles and a desired goal. A person only has an opportunity if she has a chance of achieving that goal, meanwhile opportunities are equal if each individual faces the same relevant obstacles, none insurmountable, with respect to achieving the same desirable goal. In this view, inequality of opportunity concerns the distribution of obstacles only.
Similarly, FEO requires that citizens have the same educational and economic opportunities (obstacles) regardless of whether they were born rich or poor: "In all parts of society there are to be roughly the same prospects of culture and achievement for those similarly motivated and endowed" (Rawls 2001). As such, FEO emphasizes the role of institutions, which are required to grant to all individuals equal command over resources. Basically, in Rawls' view the society is intended as a system of fair cooperation where "what has to be distributed justly -or fairlyare the benefits and burdens of social cooperation" (Sugden 1993). In this sense, optimal redistributive policies concern the distribution of social (e.g. training and education costs), not natural (e.g. talent) resources. 2 Notably, Rawls' view has been criticized by Sen (1992) as "equal command over resources can coexist with unequal real opportunities because individuals 1 Strictly speaking, Rawls proposal is a theory of 'background procedural justice' where all outcome inequalities are said to be legitimate whenever resulting from a well-ordered society. 2 The interpretation of Rawls' fair equality of opportunity as proposed in this paper is not the only existing one. According to Michelbach et al. (2003), " [Rawls] argues that individuals not only do not deserve the advantages they enjoy from wealth, connections, and other privileges, but that they similarly do not deserve any advantages from the natural lottery, such as intelligence, beauty, strength, or even the desire to work hard".
www.economics-ejournal.org 5 conomics: The Open-Access, Open-Assessment E-Journal differ in their ability to convert resources into functionings". Evidently, Sen and Rawls' views originate from two very different definitions of opportunity. In Rawls' view, an opportunity is intended as a 'chance of access to resources', whereas Sen refers to an opportunity as a 'chance of outcome' (or outcome prospect). 3 This aspect of Rawlsian justice is particularly relevant when considering FEO as one of the two criteria that outcome inequalities are required to satisfy to be regarded as legitimate. Since inequalities must "be attached to offices and positions open to all under conditions of fair equality of opportunity" (Rawls 2001), if outcome inequalities occur between individuals with the same endowment of social resources (e.g., economic conditions of parents in the early years, access to public services in the place of origin), then this inequality is said to be fair.
Here, we propose an extension of this idea by claiming that outcome inequalities are fair if and only if unequal access to social resources cannot be said to be one of the 'determinants' of inequality. In this sense, social and economic inequalities are required to be 'complaint-free' in the view of the Rawlsian ideal of social cooperation and stability, independently of the contribution of un/fairness to the single outcome gap. This is of moral importance in itself as, in this view, which clearly differs from Roemer's ideal of leveling the playing field, any pairwise outcome gap is said to be unfair even if it is partly but not entirely originating from unequal social circumstances. 4 According to this extension of Rawls' FEO, we claim that if the outcome disparity benefits the least endowed individual (e.g., with no access to same offices and positions as the other individual), it must be the case that fairness holds once again. 5 This consideration is not superfluous because outcomes, as remarked by Sen's critique above, are not uniquely generated by social resources, i.e., better outcomes might be achieved by individuals with worse endowment of social resources because of different natural resources, or even luck (e.g., Lefranc et al. 2009). 3 In a sense, this debate resembles the old distinction between formal and substantive equality of opportunity (Rosenfeld 1986). 4 As such, a distinction is made between fair and unfair disparities, independently of the monetization of the contribution of circumstances and responsible choices which is implicitly assumed for the parametric estimation of equality of opportunity (e.g., Bourguignon et al. 2007). 5 A similar procedure has been already implemented in the empirical strategy proposed by Abatemarco (2015) for the estimation of Roemer's equality of opportunity.
www.economics-ejournal.org 6 conomics: The Open-Access, Open-Assessment E-Journal So said, we claim that, in Rawls' view, pairwise outcome disparities are unfair, and so, illegitimate, if and only if the better-off individual coincides with the better endowed one in terms of social resources. On the other hand, pairwise outcome disparities are fair, and not yet legitimate (as goodness is also required), whenever the better-off individual is not the better endowed one in terms of social resources.

Difference Principle
In Rawls' view, fairness of social and economic inequalities is ruled by FEO, meanwhile goodness comes from DP. Specifically, DP poses an additional condition to be verified to make social and economic inequalities legitimate, by which social institutions be arranged so that financial inequalities are to everyone's advantage, and specifically, to the greatest advantage of those advantaged least (Wenar 2012).
Remarkably, to the extent that income inequalities are said to be good if generating benefits for the whole population, and especially for the worst-off, Rawlsian meritocracy takes into account the consequences of inequalities, besides their origins (i.e., responsibilities or circumstances). 6 As such, the theory of justice as fairness goes definitely beyond the idea of equalizing opportunities. Also, as merit is defined by considering social consequences of inequalities, not just individual ones, DP is meant to be a threat to methodological individualism characterizing most of the standard economic theory.
Drawing from DP, two major implications can be emphasized. First, DP recalls one of the most relevant debates in the economic theory, that is the identification of the 'effects of inequality on growth'. Second, since growth is required to benefit especially the worst-off, poverty is crucial. In this sense, the Rawlsian theory of justice relies, among all, on the capacity of social and economic inequalities to generate growth, which is additionally required to be of the 'pro-poor' kind.
It turns out that DP concerns the indirect effect of inequality on poverty through growth, which is not to be confused with the direct effect (e.g., Bourguignon 2005) by which any inequality reducing transfer is inevitably poverty reducing (independently of growth) when the donor is non-poor whereas the recipient is poor, and vice versa. Differently, in the Rawlsian view, inequalities are good whenever they are (i) growth enhancing, and (ii) to the greater benefit to the poorest individuals.
As such, the definition of a methodology for the empirical estimation of Rawlsian equity passes inevitably through the identification of implementable criteria by which good and bad (pairwise) inequalities can be identified according to their impact on (i) growth determinants, and (ii) pro-poor growth, which is not straightforward at all. In what follows, we consider both aspects separately.

a) Inequality on growth
In this section, we argue that any pairwise outcome inequality can be said to be growth enhancing if (i) the disparity is not jeopardizing individual opportunities to access profitable investments in terms of both human and physical capital accumulation, and (ii) the disparity enforces effort and economic incentives in general. In what follows, we offer a justification for this claim. More specifically, given the most relevant growth determinants as identified in Barro's (1998) seminal paper, 7 consequences of pairwise inequalities in terms of growth are delineated by evaluating the impact of such inequalities on each growth determinant.
According to Barro, "[long-run or steady-state level of per capita output] depends on an array of choice and environmental variables. The private sector's choices include saving rates, labor supply, and fertility rates, each of which depends on preferences and costs. The government's choices involve spending in various categories, tax rates, the extent of distortions of markets and business decisions, maintenance of the rule of law and property rights, and the degree of political freedom".
Let's consider first the effect of inequality on the saving rate. On one hand, inequality affects the saving rate by giving to few people a better and deeper chance to invest in resource-demanding activities which would not be undertaken otherwise. This applies to both physical (e.g., Kaldor 1957) and human capital (e.g., Barro 2000, Wenar 2012). On the other hand, in the presence of credit market imperfections, inequality, by enlarging the set of people who may have access to profitable investments in human and physical capital, may increase efficiency, and so generate growth (Galor and Zeira 1993). These two causalities evidently conflict with each other. However, the latter is known to dominate the former on the basis of empirical evidences. 8 Let's now turn to the second determinant of growth as indicated by Barro. Labor supply is clearly affected by inequality as well. Compressed wage structures that do not reward merit will lead to more equal societies, but it is also likely that they will reduce workers' incentives to put in additional effort or aim at outstanding achievements (Mirrlees 1971). "Good inequalities are those that reflect and reinforce market-based incentives that are needed to foster innovation, entrepreneurship and growth" (Chaudhuri and Ravallion 2006). In this sense, the principle of reward, 9 by which inequalities determined by responsible choices (e.g., effort) are legitimate (and not to be compensated), is implicitly relevant in Rawlsian justice as "institutions promote or restrict growth according to the protection they accord to effort" (Lewis 2013). Nevertheless, in contrast with Roemer's leveling of the playing field, here, rewarding effort is to be intended as a step toward meritocracy, not meritocracy itself.
Then, from the former two growth determinants (i.e., saving rate and labor supply), we can infer that pairwise inequalities are expected to affect growth through (i) individual opportunities to access profitable investments in terms of both physical and human capital accumulation, and (ii) the optimal design of eco-8 In a sequence that mirrors intellectual fashions on the empirics of growth, researchers have looked at rates of growth over long periods of time (e.g., Persson and Tabellini 1996, Perotti 1996, Alesina and Rodrik 1994, the level of income across countries (Easterly 2007), and the duration of growth spells (Berg, Ostry and Zettelmeyer 2012), and have found that inequality is associated with slower and less durable growth. The few exceptions (Forbes 2000, Banerjee andDuflo 2003) tend to pick up ambiguous short-run correlations (Aghion, Caroli, andGarcia-Penalosa 1999, Halter, Oechslin, andZweimï¿oeller 2014). According to Galor and Moav (2004), the dominating causality strongly depends on the degree of development in the society; more precisely, the positive effect of inequality is expect to prevail in developing countries only. 9 See Fleurbaey and Maniquet (2006) for different formulations of the same principle.
www.economics-ejournal.org 9 conomics: The Open-Access, Open-Assessment E-Journal nomic incentives. In addition, for the rest of the growth determinants mentioned above, the way inequality may affect growth basically replicates these two rationales. 10 b) Growth on poverty The impact of growth on poverty rates has been the object of vibrant debates among those who believe that growth is itself the best anti-poverty policy and those who argue that growth is not necessarily alleviating poverty within a market economy.
According to the first view, Dollar and Kraay (2002) show empirically that the income of the poor rises one-for-one with overall growth. 11 As such, Dollar and Kraay conclude that governments need not follow pro-poor growth policies; they should simply maximize economic growth provided they avoid high inflation and maintain fiscal discipline.
In contrast, some others have observed that economic growth in the last decades has not changed the degree of relative inequality, meaning that, the proportional benefits of growth going to the poor are the same as those enjoyed by the non-poor. According to this view, Kakwani and Pernia (2000) observe that "the growth process that results from market forces generally benefits the rich proportionally more than the poor. This is because the rich have inherent advantages (e.g., human and material capital) in a market economy".
It is evident in itself that the basic foundation of pro-poor growth is strictly related to Rawls' (1971) maximin principle. Even more, in line with Kakwani and Pernia (2000), DP clearly progresses in the direction of pro-poor growth by claiming that growth is desirable to the extent that it is to the greatest benefit of the neediest part of the population. Given Rawls' focus on pro-poor growth, it is worth observing that, within this literature, several definitions of pro-poor growth have been proposed. For some observers, growth is pro-poor if it leads to any reduction in poverty (e.g., Ravallion andChen 2003, Ravallion 2004); for others, it is pro-poor only if it leads to a disproportionate increase in the incomes of the poor, that is, if it is associated with declining inequality (e.g., White and Anderson 2000). 12 The former definition of pro-poor growth is much less strict and focuses solely on the link between poverty and growth; a growth episode is said to be pro-poor if poverty falls regardless of the developments on the inequality front. The second definition, instead, would basically require that the income share of the poor population increases. The simplest version of this definition is based on a relative concept of inequality and would simply state that the growth rate of the income of the poorest individuals is greater than the average growth rate (White and Anderson 2000). 13 To the extent that growth is to benefit more the least well off, Rawls' DP clearly evokes the latter approach, that is, growth is of the pro-poor kind if it reduces both poverty and inequality. In this sense, DP resembles the definition of the Asian Development Bank (ADB 1999) by which "growth is pro-poor when ... accompanied by policies and programs that mitigate inequalities and facilitate income and employment generation for the poor, particularly women and other 12 Specifically, the major benefit for the poorest part of the population can be defined in absolute or relative terms, depending on the use of money measures or shares (e.g., Bibi et al. 2012). 13 Another version of this definition is proposed by Kakwani and Pernia (2000) where poverty reduction and inequality improvement are taken into account simultaneously, that is, pro-poor growth is defined in such a way as to account for both (i) the impact of growth when the distribution of income does not change, and (ii) the effect of income redistribution when total income does not change.
www.economics-ejournal.org 11 conomics: The Open-Access, Open-Assessment E-Journal traditionally excluded groups". 14 The latter definition, in line with Rawls' idea of equal command over resources, emphasizes the role of opportunities of access to income and employment positions. In this sense, "[pro-poor growth is obtained by removing artificial barriers to entry into certain trades and professions, or into the formal labor market in general ... [through] adequate public spending for basic education, health and family planning services, improved access to credit, and the promotion of small and medium enterprises" (Kakwani and Pernia 2000).
As such, we argue that in order to generate pro-poor growth, pairwise outcome inequalities must not be jeopardizing the opportunities of access to profitable investments in human and physical capital accumulation. As this statement is the same as the first condition obtained in the previous section (i.e., for pairwise inequalities to be growth enhancing), in our view, growth-enhancing pairwise inequalities are generally expected to generate growth of the pro-poor kind (not vice versa). Notably, this does not mean that growth is generally pro-poor (i.e., pro-poor growth policies are useless), but that growth originating from pairwise inequalities is always pro-poor.
Summing up, according to our interpretation of Rawlsian justice, pairwise outcome inequalities are good by DP (not necessarily legitimate), if (i) disparities enforce effort and economic incentives, and (ii) disparities do not jeopardize individual opportunities to access profitable investments in terms of both human and physical capital accumulation. In addition, to be legitimate, pairwise outcome disparities are required (iii) to be fair by FEO, that is, the better-off individual must not be the better endowed one in terms of command over (social) resources.

Formal Definitions
Given a population of N individuals, let {y 1 , ..., y N } ∈ ℜ N + be the increasingly ordered outcome vector where y is the socioeconomic variable which, without loss of generality, may be intended as income.
Each individual is associated with a set of z n natural circumstances {n 1 , ..., n z n } identifying genetic traits (e.g., gender, cognitive abilities). Moreover, each individual is characterized by a finite set of social circumstances {s 1 , ..., s z s } indicating the social environment in the early years (e.g., parental income, access to public services/facilities). Evidently, both natural and social circumstances are intended as beyond individual control.
For each natural circumstance, let n q := {n 1 q , ..., n τ q q } be the vector indicating τ q mutually exclusive discrete values (e.g., male or female) associated to the qth natural circumstance variable (e.g., gender). Similarly, let s q := {s 1 q , ..., s τ q q } be the vector indicating τ q mutually exclusive discrete values (e.g., high/medium/low) associated to the qth social circumstance variable (e.g., parental income).
We define the ith natural opportunity type (θ n i ) as a combination of discrete values (e.g., male and Hispanic) associated with each natural circumstance variable (e.g., gender and cognitive abilities), i.e. θ n i = (n α 1 ∩ ... ∩ n ω z n ). Similarly, the ith social opportunity type (θ s i ) is defined as a combination of discrete values (e.g., low parental income and high public services performances) associated with each social circumstance variable (e.g., gender and cognitive abilities), i.e. θ s i = (s α 1 ∩ ... ∩ s ω z s ). Given the finite set of natural opportunity types Θ n := {{θ n i }n i=1 } and social opportunity types Θ s := {{θ s i }s i=1 }, let define with Θ := {{θ n i }n i=1 , {θ s j }s j=1 } the finite set of opportunity profiles, each one indicating a single natural and social opportunity type respectively, which can be reformulated as Θ := {θ k }n ×s k=1 . E.g., if natural circumstances consist of gender (male or female) and cognitive abilities (high or low), whereas social circumstances are parental income (low or high) and public services performances in the place of origin (low or high), then n = (2) 2 ands = (2) 2 . In addition, the set of opportunity profiles consists of (n ×s) = (2) 2 × (2) 2 = (2) 4 different opportunity types.
Given the opportunity types, individuals may also differ from each other with www.economics-ejournal.org 13 conomics: The Open-Access, Open-Assessment E-Journal respect to their responsibility type (e.g., effort). More specifically, let E := {e i }ē i=1 be the finite set of responsibility types. We assume that y = f (θ n , θ s , e) is the income generating function where f : Θ n × Θ s × E → ℜ + . Evidently, income is expected to increase when natural or social opportunity type improves, as well as when the responsibility type is better. As such, the definition of an empirical strategy crucially depends on the identification of both opportunity and responsibility orderings, that is not straightforward as strong assumptions are inevitably required.
In what follows, we opt for an ordinal pragmatic approach. 15

Opportunity Orderings
Given the vector indicating τ q mutually exclusive discrete values (e.g., high or low cognitive abilities, male or female) associated to the qth natural circumstance variable (e.g., cognitive abilities, gender), i.e. n q := {n 1 q , ..., n τ q q }, we assume that discrete values can be completely ordered in terms of propitiousness within the income generating process (e.g., high cognitive abilities more propitious than low ones) independent of other circumstances and responsible choices. Formally, this means that, holding fixed the rest of the natural and social circumstance variables and the responsibility type, for each pair of values {n α q , n β q } (originating the two natural opportunity types θ n i and θ n j respectively), and according to existing social conditions (which may differ over time and across geographical areas), one may reasonably expect either y θ n i ,θ s ,ē = f (θ n i ,θ s ,ē) > f (θ n j ,θ s ,ē) = y θ n j ,θ s ,ē ∀ē,θ s , or y θ n i ,θ s ,ē = f (θ n i ,θ s ,ē) < f (θ n j ,θ s ,ē) = y θ n j ,θ s ,ē ∀ē,θ s . 16 Given a complete ordering among discrete values associated to each natural 15 For cardinal approaches quantifying the contribution of effort and circumstance within the income generating function see, Bourguignon et al. (2007), Checchi et al. (2008), Pistolesi (2009), Ferreira and Gignoux (2011), and Almas et al. (2011. 16 Even if the possibility of orderings of opportunity sets has been already considered in the existing literature (e.g., Kranich 1996, Ok 1997, Weymark 2003, the possibility of a direct measure of the propitiousness of circumstances is not straightforward. However, to the extent that circumstances, effort and outcomes are observable ex-post, one may capture the impact of circumstances so as to infer (indirectly) a propitiousness ordering. This is not very distant from Rawls' idea about the impossibility of measuring native natural endowments as opposed to (measurable) realized abilities and talent Rawls (2001), as the propitiousness of native circumstances cannot be rigorously measured ex-ante, independently of the design of social institutions.
www.economics-ejournal.org 14 conomics: The Open-Access, Open-Assessment E-Journal circumstance, let {θ n 1 , ..., θ n n } be the set of natural opportunity profiles and let y i jk indicate the income unit with the ith natural opportunity type, the jth social opportunity type and the kth responsibility type. We define the partial natural opportunity ordering n θ as follows: (i) y i jk n θ y m jk , whenever θ n i can be obtained from θ n m by selecting more propitious values for some natural circumstance variable(s) without worsening any other, and (ii) y i jk || n θ y m jk (non-comparability), whenever θ n i can be obtained from θ n m by selecting more propitious values for some natural circumstance variable(s) but less propitious for some other(s). We write n θ and ∼ n θ to indicate the asymmetric and symmetric component of the natural opportunity ordering respectively.
For instance, let cognitive abilities (high, low) and gender (male, female) be the only two (binary) natural circumstance variables. Since being 'high' and 'male' is usually found to be more propitious in the income generating process, then, by virtue of the natural opportunity ordering above, 'low'-'males' benefit of a better natural opportunity type with respect to 'low'-'females', but the former is not comparable with the natural opportunity type consisting of 'high'-'females'.
Evidently, the same formal framework can be replicated for social circumstance variables. Once again, we assume that discrete values (e.g., high or low)) associated to the qth social circumstance variable (e.g., parental income in the early years) can be completely ordered in terms of propitiousness within the income generating process, independently of other circumstances and responsible choices. Formally, holding fixed the rest of the natural and social circumstance variables and the responsibility type, for each pair of values {s α q , s β q } -originating the two social opportunity types θ s i and θ s j respectively -it is reasonable to expect, on a priori grounds, either yθn ,θ s i ,ē = f (θ n ,θ s ,ē) > f (θ n j , θ s j ,ē) = yθn ,θ s j ,ē ∀ē,θ n , or yθn ,θ s i ,ē = f (θ n , θ s i ,ē) < f (θ n , θ s j ,ē) = yθn ,θ s j ,ē ∀ē,θ n . Let {θ s 1 , ..., θ s s } be the set of natural opportunity profiles. The partial social opportunity ordering s θ is defined as follows: (i) y i jk s θ y iok , whenever θ s i can be obtained from θ s o by selecting more propitious values for some social circumstance variable(s) without worsening any other, and (ii) y i jk || s θ y iok (non-comparability), whenever θ s i can be obtained from θ s o by selecting more propitious values for some circumstance variable(s) but less propitious some other(s). We write s θ and ∼ s θ to indicate the asymmetric and symmetric component of the social opportunity www.economics-ejournal.org ordering respectively. Finally, let's recall the finite set of opportunity profiles Θ := {{θ n i }n i=1 , {θ s j }s j=1 }. We define the opportunity profiles ordering θ as follows: (i) y i jk θ y mok , whenever y i jk n θ y mok and y i jk s θ y mok with at least one of the two preferences holding strictly, (ii) y i jk || θ y mok (non-comparability), whenever y i jk n θ y mok and y i jk ≺ s θ y mok , or y i jk ≺ n θ y mok and y i jk s θ y mok , or y i jk || n θ y mok , or y i jk || s θ y mok . Once again, we write θ and ∼ θ to indicate the asymmetric and symmetric component of the opportunity profiles ordering respectively.

Responsibility Ordering
In line with Roemer's (1993) pragmatic theory, if a disjoint and exhaustive partition rule is assumed to exist by which individuals within the same population can be grouped depending on the opportunity profile (accounting for both natural and social circumstances), two individuals belonging to different subgroups are said to be comparable in terms of responsible choices (not necessarily the same degree of responsibility) if they are equally ranked in the respective subgroup income distributions. In this sense, the income gap among equally ranked individuals may capture the contribution of circumstances to overall inequality.
Here, a more demanding pragmatic approach is proposed by which rank-based partial responsibility orderings are defined (Abatemarco 2010). Given the disjoint and exhaustive partition of the population with respect to the finite set of opportunity profiles Θ := {θ k }n ×s k=1 , let F k (y) be the subgroup cumulative frequency distribution associated to the kth opportunity profile. Let φ (·) be a monotone transformation and y ik the income of the ith individual associated to the kth opportunity profile, we identify the responsibility type of y ik with the interval φ [F k (y i−1,k )] < e ik ≤ φ [F k (y ik )]. As such, the partial responsibility ordering e can be (pragmatically) defined as follows: and F k (y ik ) = F h (y jh ) then y ik ∼ e y jh , and (d) the income units are non-responsibility comparable otherwise (y ik || e y jh ). 17 The asymmetric component of the responsibility ordering is indicated by e .
Within the rank-based approach, since individuals belonging to the same subgroup are characterized by the same opportunity type, within-group income gaps are unequivocally ascribed to different responsible choices. As such, rank-based responsibility orderings allow to overcome very information demanding processes which would inevitably be required otherwise. However, this is not a free-meal. To the extent that some circumstances may be unobservable at reasonable costs, individuals within the same subgroup may indeed differ from each other in terms of circumstances, and the rank-based ordering would erroneously legitimate such income disparities in the name of nonexisting differences in terms of responsible choices. This is a relevant problem which is known to afflict both parametric and non-parametric estimation strategies (Ramos and Van de gaer 2012). In this context, we argue that partial responsibility orderings are definitely to be preferred with respect to complete ones, as this may allow the mitigation of distortions originating from unobserved circumstances.
An additional consideration concerns the indirect effect of circumstances; it is known that responsible choices may be significantly influenced by circumstances (e.g., Bourguignon et al. 2007). In this sense, it is worth observing that the rankbased approach automatically accounts for the indirect effect because responsibility orderings are invariant with respect to both translations and scale transformations applied to each subgroup.

Fairness and Goodness
According to FEO, pairwise income inequalities are fair whenever the better-off individual did not enjoy any advantage in terms of access to social resources; as we said above, in line with the Rawlsian ideal of social cooperation, we assume that fairness holds if the disparity is complaint-free in terms of command over social resources, whatever the size of the contribution of unfairness to the income gap. As such, fairness of pairwise income inequalities can be defined as follows.
Definition 3.1 (Fairness) Given the finite set of social opportunity types Θ s := {θ s i }s i=1 and the income distribution {y 1 , ..., y N } ∈ ℜ N + with y j > y i , rank-based approach generates complete responsibility orderings in the presence of equally sized subgroups.
www.economics-ejournal.org 17 conomics: The Open-Access, Open-Assessment E-Journal 3.1.i) if y j s θ y i , then |y j − y i | is fair; 3.1.ii) if y j s θ y i or y j || s θ y i , then |y j − y i | is not fair. To the extent that the sole social circumstance variables are accounted for, Rawlsian fairness in Definition 3.1 differs with respect to the standard compensation principle for two reasons at least. First, Rawlsian fairness is not sufficient to claim legitimacy of an income gap, and so compensation deservingness. Second, natural circumstances are not accounted at all, as fairness is uniquely concerned with institutions intended as a system of fair cooperation.
Rawlsian fairness is a necessary but not sufficient condition for legitimacy of pairwise inequalities, as the additional criterion to be considered for sufficiency purposes is goodness. In turn, as argued above, by virtue of DP, two necessary conditions are required for goodness, i.e. (i) income disparities must enforce effort and economic incentives (hereafter, incentive-based goodness), and (ii) income disparities must not jeopardize individual opportunities to access profitable investments in terms of both human and physical capital accumulation (hereafter, access-based goodness). Remarkably, the simultaneous verification of both conditions is sufficient and necessary for an income disparity to be good.
Definition 3.2 (Incentive-based Goodness) Given the finite set of opportunity profiles Θ := {θ i }n ×s i=1 and the income distribution {y 1 , ..., y N } ∈ ℜ N + with y j > y i , 3.2.i) if y j e y i , then |y j − y i | is good for incentives; 3.2.ii) if y j e y i , or y j || e y i , then |y j − y i | is not good for incentives.
As such, Definition 3.2 resembles the principle of reward as intended by Arneson's (1999) strict egalitarianism of opportunity, where maximum equality of opportunity is obtained if "no one is worse off than others through no fault or voluntary choice of her own". Notice that, to be coherent with Rawlsian framework, reward has not to be regarded as the legitimate prize for better individual responsible choices. Here, reward is borne to the extent that it represents an incentive to better responsible choices, which are expected to be growth enhancing in the interest of the society as a whole. Most importantly, a legitimate prize does not need to be incentivizing, and vice versa.
In addition, as compared to alternative definitions of the reward principle (e.g., Fleurbaey and Maniquet 2006), Definition 3.2 better suits the ordinal approach to responsible choices and circumstances we have opted for, because a distinction is made between good and non-good income disparities without any possibility to separate the good from the non-good component in every single income gap. Differently, to the extent that the contribution of circumstances and responsible choices within the income function is monetized (i.e., parametric approach), good inequalities may be identified according to the principle of natural reward, by which the effect of heterogeneous circumstances are to be canceled out across the entire population, or, alternatively, according to the principle of utilitarian reward, by which heterogeneous circumstances are to be canceled out across equally deserving individuals in such a way as to maximize the sum of individual utilities.
Moving a step forward, as observed above, in order to be good, pairwise income inequalities are additionally required to be not jeopardizing individual opportunities to access profitable investments in terms of both human and physical capital accumulation. The very basic question to be answered is the following: when do pairwise income inequalities jeopardize individual opportunities of access?
Evidently, an answer to this question cannot be given independently of a definition of access opportunities.
From a methodological point of view, opportunities of access can be differently defined depending on the main objectives. For instance, within a strictly dichotomic approach, one may say that two individuals differ in terms of opportunities of access when access is granted to one but not to the other. However, if the dichotomic approach is abandoned, opportunities of access may still differ in magnitude even if access is granted to both individuals.
In this paper, as we aim at separating pairwise inequalities which jeopardize access opportunities from the rest of pairwise inequalities, we opt for the former approach, that is, we claim that access is not granted for socially excluded individuals, and vice versa (i.e., it is the status of poor that really matters, not the size of the poverty gap). As such, access-based goodness can be formally defined as follows.
Definition 3.3 (Access-based Goodness) Given the income distribution {y 1 , ..., y N } ∈ ℜ N + with y j > y i , let z be the poverty line capturing social exclusion in the society, 3.3.i) if y i > z, or y j ≤ z, then |y j − y i | is not bad for access; 3.3.ii) if y j > z and y i ≤ z, then |y j − y i | is bad for access.
Basically, by Definition 3.3, any pairwise income inequality jeopardizes access opportunities for one of the two individuals whenever the income disparity is associated with an access disparity as well. On the contrary, if the income disparity does not concur with an access disparity, then such inequality is not said to be jeopardizing access. Intuitively, goodness cannot hold whenever the income disparity can be said to be contributing to the generation of access disparities. Remarkably, by claiming that a necessary (but not sufficient) condition to legitimize social and economic inequalities is that such a disparity should be not responsible for poorness, our interpretation of DP principle is coherent with Rawlsian maximin principle. 18

Gini-based Aggregation
Recalling formal definitions in the previous Section, Ralwsian equity can be reformulated as follows. As compared to egalitarianism of opportunity, social and economic inequalities are said to be legitimate to the extent that rewarding effort at the individual level, that is assumed to be growth enhancing, is not poverty enhancing, given that fair equality of opportunity has been granted. 19 According to Definition 3.4, inequity is given by the aggregation of income gaps satisfying condition (II), meaning that equity differs from equality due to legitimate income inequalities (I). Specifically, for measurement purposes, in line with the old tradition of the Gini index, we opted for the unweighted aggregation of income gaps, even if weighted aggregation functions may be supported as well.
Let Ω be the set of pairwise income gaps satisfying conditions (I) in Definition 3.4, given income distribution {y 1 , ..., y N } ∈ ℜ N + , inequality is measured as, where µ stands for mean income. Most importantly, following the same logic behind Dagum's (1997) decomposition (two-components), G can be decomposed as follows where the second component in squared brackets captures inequity. As such, we measure Rawlsian inequity (G R ) as where the contribution of Rawlsian inequity to overall inequality is defined as The inequity index G R (and G c R ) is scale invariant, partially symmetric in Cowell's (1980) sense, and defined in [0, 1]. In addition, it is replication invariant to the extent that a k-fold replication of the entire population refers to all the characteristics of each income unit (i.e., income, responsibility type, social opportunity type).
Any non-reranking rich-to-poor transfer (hereafter, PD transfer) between y k and y h is inequity reducing whenever h, k ∈ ω. Also, it can be shown that, given y k > y h with k ∈ Ω and h ∈ Ω, any PD transfer is inequity reducing whenever y h <ỹ with y indicating the median income for all i ∈ Ω. Similarly, given y k > y h with k ∈ Ω and h ∈ Ω, any PD transfer is inequity reducing whenever y k >ỹ withỹ indicating www.economics-ejournal.org 21 conomics: The Open-Access, Open-Assessment E-Journal the median income for all i ∈ Ω. According to this framework, it must be the case that inequity is null when inequality is null, but not vice versa. Mostly, perfect equity may be attained in the presence of social and economic inequalities. Proposition 3.1 makes the point. i Proof 3.1 Given θ i = θ j if and only if θ n i = θ n j , it must be y i ∼ s θ y j ∀ i, j by which (3.1.i) holds for all |y j − y i |. Similarly, if y i ≥ z ∀ i, or y i < z ∀ i, then (3.3.i) holds for all |y j − y i |. Finally, if each subgroup, as obtained through a disjoint and exhaustive partition w.r.t. {θ i }n ×s i=1 , is the k-fold replication of another subgroup, then y i = y j ∀ i, j : y i ∼ e y j and y j > y i ∀ i, j : y j e y i . As such, (3.2.i) holds for all |y j − y i |. This proves that G R = 0. On the other hand, given {y 1 , ..., y N } ∈ ℜ N + such that ∃i : y i = y j (i.e., G = 0), if G R = 0, we prove that all pairwise income inequalities must be Rawlsian equitable according to Definition 3.4. Given G R = 0, by (3.2.ii), if y j ∼ e y i , or y j || e y i , then it must be y j = y i ∀ i, j. As such, by definition of ≺ e , if {y 1 , ..., y N } ∈ ℜ N + is such that ∃i : y i = y j , then each subgroup associated to an opportunity profile must be the k-fold replication of another subgroup. Indicating by N i the size of the ith subgroup, this ensures that N j = k j N i for all subgroups, with k j being any positive integer. By (3.3.ii), |y j − y i | = 0 whenever y j ≥ z > y i , which is possible if and only if all y i ≥ z ∀ i, or y i < z ∀ i. Finally, given that (i) {y 1 , ..., y N } ∈ ℜ N + is such that ∃i : y i = y j , (ii) i, j ∈ θ k implies i, j ∈ θ s h ∀ i, j, k, h, and (iii) each subgroup is the k-fold replication of another subgroup, let's assume, by contradiction, that ∃i, j : y j s θ y i , or y j || s θ y i (i.e., (3.1.ii)), by which two subgroups differ from each other with respect to θ s . It is clear that, if each subgroup consists of more than one individual, there must exist www.economics-ejournal.org 22 conomics: The Open-Access, Open-Assessment E-Journal at least one unfair inequality, which would contradict G R = 0. As such, it must be the case that y i ∼ s θ y j ∀ i, j.
Proposition 3.1 emphasizes that within the Rawlsian view, the focus is on a social system of fair cooperation where the same opportunities of investments in human and physical capital must be granted to everybody. In addition, in line with a broader interpretation of the maximin principle, equity is maximized when there is no group of more disadvantaged individuals, or, equivalently, all of them are disadvantaged. Finally, given these two conditions above, inequalities can be tolerated if and only if these are determined by effort in such a way as to be growth but not poverty enhancing. In this sense, as compared to Roemer's ideal of leveling the playing field, the applicability of the principle of reward is restricted a priori by additional normative requirements concerning the consequences of income disparities.

Data
The PSID 20 is used to compare US income distributions over time in terms of Rawlsian equity as defined above. This database has been preferred due to (i) the availability of information on most of the natural and social circumstance variables, and (ii) the high number of records. The former aspect is crucial because, as we observed above, omitted variables may cause the misleading legitimation of illegitimate income gaps, which may seriously jeopardize the reliability of major empirical findings (Ramos and van de Gaer 2012). The latter aspect is crucial as well; to the extent that the initial population is to be partitioned into several subgroups, a high number of observations is required to ensure a sufficient number of records in each subgroup (Ferreira and Gignoux 2011).
To facilitate the comparison with the existing empirical literature, we consider the same initial wave as in Abatemarco (2015), where the evolution of equality of opportunity in the US is measured according to Roemer's idea of leveling the playing field. More specifically, eight waves are considered from 1999 to 2013 (1999, 2001, 2003, 2005, 2007, 2009, 2011, 2013). 21 We refer to the sole population of heads aged less than 80 years old. Evidently, the estimation of the impact of circumstance and effort variables on the income generating function requires a population of individuals, not households. In addition, we choose to focus on the sole population of heads because (i) the decisions of non-heads are usually more influenced by family needs than heads' ones, and (ii) some variables are not available for non-heads (e.g., taxable income).
Income is measured in disposable terms. More specifically, disposable income is defined as total income from labor and capital investments plus public (monetary) transfers minus income and property taxes. 22 Poverty thresholds for each wave are taken from publicly available data of the US Census Bureau. 23 According to the distinction between natural and social circumstances, we consider four natural circumstance variables, i.e. gender, health status in the early years (before 16-17 years old), ethnicity, and IQ score 24 , and two social circumstance variables, i.e. economic situation of parents in the early years, and place of origin in the early years. 25 Remarkably, we consider health status in the early years and not current health, as (i) the latter is more informative about chances given to each individual to invest 21 Income data refer to the previous chronological year (e.g., 1999 income records refer to 1998). 22 Total income is determined by head's income from labor, asset, trust fund, dividends, and interest. To account for the Federal Income Tax, brackets and tax rates from 1998 to 2012 have been considered. The property tax is entirely imputed to the head when single, whereas it is halved for married heads. To save as many observations as possible, missing values for each income variable (e.g. 1999) have been been replaced by the corresponding value of the same respondent as resulting from the subsequent wave (e.g. 2001) if available. Finally, outliers in the distribution of disposable income have been dropped by eliminating observations below and above the 5th and the 95th centile respectively (e.g. Jarvis and Jenkins 1998). 23 Data for unrelated individuals available at https://www.census.gov/hhes/www/poverty/data/threshld/. 24 The introduction of a proxy for cognitive abilities (IQ test) within the set of circumstance variables is not straightforward from a philosophical point of view because a trade-off may occur between different social and ethical objectives, that is, the"above notion of equality of opportunity may contradict other ethical principles such as self-ownership and freedom" (Lefranc et al. 2008). 25 To preserve a sufficient number of observations, missing values are replaced by records available from other waves for the same variable and individual.
www.economics-ejournal.org 24 conomics: The Open-Access, Open-Assessment E-Journal in human capital accumulation, and (ii) it is less influenced by responsible choices even if, as observed by Sen (2002), the impact of responsible choices may be ambiguous in this field "since we tend to give priority to good health when we have the real opportunity to choose". In addition, as compared to Abatemarco (2015), for our purposes the place of origin is not considered in terms of employment opportunities (i.e. unemployment rate in the place of origin in the early years), but as the characterization of opportunities given to an individual to invest in human capital accumulation whenever willing to. This aspect is captured by using information on the degree of urbanization in the place where the respondent grew up (i.e., farm, rural area, small town, large city). Binary circumstance variables are defined even if, except for gender, more than two alternatives are available from the PSID. This choice is to be intended as a compromise aimed at minimizing the loss of information. On the one hand, an increase in the number of alternatives for each variable would grant more precise information at the individual level. On the other hand, the number of subgroups would exponentially increase with a serious loss of information due to the lack of statistical significance for many subgroups.
As such, 64 subgroups are generated from the combination of six binary circumstances: gender ( 26 To construct each subgroup, both the PSID family and the PSID individual data files have been used. Cross-sectional sample weights have been considered for each wave. The health variable is slightly changed across waves. From 1999 to 2003 the health variable has been used to distinguish individuals reporting "excellent" and "very good" health with respect to the remaining population answering "good", "fair", or "poor". This definition of the binary variable is mostly expected to identify individuals with no health problems at all. Remarkably, starting from 2005 the questionnaire strongly changed for health in the early years. Individuals are no longer asked about their generic health conditions in the early years, but if they had specific health problems. We assume that health in the early years was not good in the presence of: missed a month or more of school due to health problems, difficulty seeing even with eyeglasses, or diabetes, or chronic ear problems or infections, or epilepsy, or severe headaches/migraines or high blood pressure. For the sole 2005, missing questions are covered by using available information for the same respondent in subsequent waves. With respect to ethnicity, a separating line is drawn between income units reporting "American" or "national origin" www.economics-ejournal.org 25

conomics: The Open-Access, Open-Assessment E-Journal
Subgroups with less than five observations have been disregarded. The number of observations varies across waves from a minimum of 4,999 to a maximum of 6,146 records, which is enough to grant statistical significance of the results. 27 In addition, from 1999 to 2013, the population consists of 66-69% male, 76-81% had no health problems, 21-27% pretty well-off parents, 50-66% are of a propitious ethnicity, 55-57% showed high IQ scores and 37-40% were from highly urbanized areas.
The average disposable income is 27.422 USD in 1999, 29,796 USD in 2001, 29,794 USD in 2003, 31,542 USD in 2005, 34,474 USD in 2007, 35,148 USD in 2009, 32,741 USD in 2011, and 33,962 USD in 2013. Given the focus on the population of heads, these statistics confirm previous evidences in the existing literature (Heathcote et al. 2009).
Income data are disaggregated at the subgroup level in Table 1, where subgroups are grouped on the basis of the number of favorable circumstances from the betteroff to the worst-off. Reasonably, subgroup average income is increasing with the number of favorable circumstances. More specifically, to highlight the contribution of each circumstance variable, correlation matrices have been computed between circumstance variables and disposable income (Table A.1, Appendix). By the latter, (e.g., French, German) or "religious" (e.g., Jewish, Catholic) and the others reporting "hyphenated American", "non-specific Hispanic identify", "racial" or "other". This partition is supported by empirical evidence on average disposable incomes for each group (Abatemarco 2015). IQ test records are obtained from the family data file for the 1968 and the 1972 waves. The latter variables have been associated with the corresponding income units from the 1999 to the 2013 waves using family, not person identifier, i.e., the IQ score is not referred to the single individual but the family. The IQ score is assumed to be low whenever (i) family has been interviewed in both waves, obtaining a score that is below the median score in both waves, or (ii) family has been interviewed in one of the two waves and is positioned below the median score. For the economic situation of parents in the early years, the population has been partitioned by drawing a separating line between individuals reporting "pretty well off" and the remaining population answering "poor" or "average". This definition is primarily aimed at the identification of true benefits in the income generating process due to family origins. Finally, the place of origin is assumed to limit access to profitable investment in human capital if individuals grew up in a "farm", or "rural area", "suburb", or "small town" as compared to opportunities offered by "large cities". 27 Subgroups with less than five observations are considered statistically insignificant and are eliminated from the computation. This condition occurs for two subgroups only in 1999 wave, i.e. FHEĪWU and FHEĪWŪ. it turns out that natural circumstance variables are much more relevant than social ones within the income generating process. Remarkably, the degree of urbanization in the place of origin and economic conditions of parents in the early years seem to have a non-significant impact on disposable income.

Results
In this section, we discuss the results of the empirical methodology we have proposed for the estimation of Rawlsian inequity. As such, we do not discuss immediate policy implications as this would go beyond the scopes of this paper. On the contrary, the reliability of our results is verified by considering previous evidences on inequality of outcomes and opportunities in the US. The US Gini index for the distribution of disposable incomes is usually found to be between 0.36 and 0.38 from 1998 to 2004 (Gottschalk and Smeeding 2000;Heathcote et al. 2009 heads aged, on average, between 42 and 44 years old, the Gini index is found between 0.405 and 0.419 from 1999 to 2013 (Table 2). This result is consistent with previous findings in Heathcote et al. (2009), where inequality is found to be sensibly larger in the population of singles 28 (income pooling within married households reduces inequality) and is increasing with the age of the sample (early retirements and the experience wage premium usually increase inequality).
As reported in Table 2, Rawlsian inequity from 1999 to 2013 is found to be between 55.7% and 64.9% of the overall inequality. This result sensibly differs with respect to previous parametric and non-parametric empirical evidences for Roemer's inequality of opportunity, which is usually found between 15% and 20% (Abatemarco 2015, Pistolesi 2009). Nevertheless, this is just what one may expect; Roemer's view is grounded on the legitimation of income gaps with respect to the sole origins of inequality, whereas Rawlsian inequity is defined by accounting for both the origins and the implications of income inequality.
Additional information can be obtained by considering the dynamics of inequity from 1999 to 2013. Starting from 2007, a rapid increase in the absolute and relative amount of inequity can be observed. This is evidently determined by the financial crisis in 2007, whose major effects are detected since 2009. The main rationale behind the impact of this crisis on Rawlsian inequity appears immediately from Table 3, where the contribution of FEO and DP are computed separately. 29 Both FEO and DP have sensibly increased in the latter three waves. However, 28 Evidently, the population of singles is not the same as the population of heads, but the latter definitely accentuates the share of singles. 29 We report the contribution of FEO and DP, as considered separately, and not the decomposition of the Rawlsian inequity index, which is not decomposable. This is evident itself when observing that the sum of the two components taken separately do not sum up to the overall index of Rawlsian inequity.
www.economics-ejournal.org 28 by considering separately the contribution of "incentive-based goodness" (DP1) and "access-based goodness" (DP2), it can be observed that the financial crisis has mostly worsened the existing poverty conditions, so that a larger share of income inequality is found to cause social exclusion and limited access to profitable investments in human and physical capital.
Remarkably, in addition to the (expected) impact of the financial crisis on poverty, and so Rawlsian inequity, Table 3 also highlights a relevant contribution of FEO, whose increase from 1999 is even stronger than that of DP. According to our framework, this means that the financial crisis has been paid relatively more by individuals with poor parental origins in rural areas. Finally, the U-shaped pattern of DP1 in Table 2 suggests that the financial crisis has seriously jeopardized the capacity of the economic system to reward better responsible choices. A discussion on the motivations of this result, although of crucial importance for the design of optimal redistributive policies, is beyond the aims of this paper. For our purposes, it is enough observe that this result confirms previous evidences on the U-shaped pattern of Roemer's inequality of opportunity (Abatemarco 2015).

Conclusive Remarks
Equality is a neutral concept whose interpretation in statistical and normative terms is straightforward. Equity, instead, inevitably inherits value judgments on the distinction between fair/good and unfair/bad inequalities. To the extent that no valid judgments are agreed upon by which some inequalities may be said to be fair/good, or some equalities are said to be unfair/bad, equality is said to be equitable or just.
In the recent times, most of the research effort in the empirical literature has been devoted to the estimation of inequality of opportunity, meanwhile Rawls' ideal of a system of fair cooperation aimed at social and political stability has been mostly disregarded in this sense. The success of egalitarianism of opportunity is somehow related to the increasing concern for 'individual responsibility' characterizing the Protestant culture (Fleurbaey 2001). Nevertheless, to the extent that egalitarianism of opportunity characterizes Rawlsian theory as well, we suggest that such a minor interest for Rawlsian Principle of Equality can be better motivated by theoretical impediments in accommodating the Difference Principle within the standard economic theory.
In this paper, Rawlsian Fair Equality of Opportunity and Difference Principle have been interpreted in such a way as to render Rawlsian equity pragmatically workable within an empirical setting. Undeniably, Rawls' theory of justice is less user-friendly and much more information demanding than other approaches, but, to our opinion, this should not be a valid reason for abandonment.
A methodology for non-parametric estimation of Rawlsian inequity has been proposed. The latter approach has been implemented to calculate the contribution of Rawlsian inequity to overall income inequality in the USA from 1999 to 2013. Iniquitous income disparities are found to account for 56-65% of overall outcome inequality, which more than doubles the usual 15-20% of iniquitous income disparities as estimated for Roemer's inequality of opportunity (Abatemarco 2013, Pistolesi 2009). Even worse, our analysis suggests that, due to the recent financial and economic crisis, the huge amount of inequity is found to be rapidly increasing in the last waves.
From a policy perspective, we wish to emphasize two major aspects. First, as it appears from our empirical findings, distributive inequity is a very relevant problem, and, today more than yesterday, policy-makers should take better care of the promotion of equity in the income distribution. Second, egalitarian policies cannot be aimed exclusively at the promotion of equality of opportunity intended as the compensation of outcome inequalities due to circumstances, and legitimation of inequalities originating from responsible choices. This is valuable but risky, 0.14 0.09