metadata: authors: 0: author: Roemer, John E.
count: Europe
docna: 0: docna: Economic development as opportunity equalization
docty: Policy Research Working Paper
subtopic: Judicial System Reform,Population & Development,Educational Sciences,Poverty Reduction Strategies
teratopic: Macroeconomics and Economic Growth,Health, Nutrition and Population,Poverty Reduction
abstracts: cdata!: Economic development should be conceived
            of as the degree to which an economy has implemented an
            efficient and just distribution of economic resources. The
            ubiquitous measure of GDP per capita reflects a utilitarian
            conception of justice, where individual utility is defined
            as personal income, and social welfare is the average of
            utilities in a population. A more attractive conception of
            justice is opportunity-equalization. Here, a two-dimensional
            measure of economic development is proposed, based upon
            viewing individuals incomes as a consequence of
            circumstances, effort, and policy. The first dimension is
            the average income level of those in the society with the
            most disadvantaged circumstances, and the second dimension
            is the degree to which total income inequality is due to
            differential effort, as opposed to differential
            circumstances. This pair of numbers is computed for a set of
            22 European countries. No country dominates all others on
            both dimensions. The two-dimensional measure induces a
            partial ordering of countries with respect to development.
repnme: repnme: Economic development as opportunity equalization
display_title: Economic development as opportunity equalization
listing_relative_url: /research/2013/07/18006010/economic-development-opportunity-equalization
topicv3: Justice m1326106 840,Education m1327048 470,Equality of Opportunities m1327180 1167,Income Inequality m1503891 2668,Life Expectancy m1504363 2666
publishtoextweb_dt: 2013-07-01T00:00:00Z
historic_topic: Macroeconomics and Economic Growth,Health, Nutrition and Population,Poverty Reduction
no_of_pages: 48
model_extractions: WPS6530 Policy Research Working Paper 6530 Economic Development As Opportunity Equalization _John E. Roemer_ The World Bank Development Economics Vice Presidency Partnerships, Capacity Building Unit July 2013
Policy Research Working Paper 6530

# **Abstract**

Economic development should be conceived of as the degree to which an economy has implemented an efficient and just distribution of economic resources. The ubiquitous measure of GDP per capita reflects a utilitarian conception of justice, where individual utility is defined as personal income, and social welfare is the average of utilities in a population. A more attractive conception of justice is opportunity-equalization. Here, a two-dimensional measure of economic development is proposed, based upon viewing individuals’ incomes as a consequence of circumstances, effort, and policy. The first dimension is the average income level of those in the society with the most disadvantaged circumstances, and the second dimension is the degree to which total income inequality is due to differential effort, as opposed to differential circumstances. This pair of numbers is computed for a set of 22 European countries. No country dominates all others on both dimensions. The two-dimensional measure induces a partial ordering of countries with respect to development.

This paper is a product of the Partnerships, Capacity Building Unit, Development Economics Vice Presidency. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at john.roemer@yale.edu.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **“Economic development as opportunity equalization”**

by John E. Roemer<sup>*</sup> Yale University Key words: economic development, equality of opportunity JEL categories: O1, D3, D63 Sector Board: Economic Policy (EPOL) and Poverty Reduction (POV)

* John Roemer is a professor of political science and economics at Yale University; his e- mail address is <u>john.roemer@yale.edu</u> I am grateful to referees of this journal for suggestions leading to important revisions, and to the many scholars with whom I have discussed these ideas.  This article is based upon a lecture given at the ABCDE meeting in Paris, 2011.
2

# 1. <u>Introduction</u><sup><u>1</u></sup>

Suppose we are concerned with the inequalities that exist in a society with respect to the distribution of some desirable good or advantage – wealth, life expectancy, literacy, or wage-earning capacity. The causes of inequality in that distribution can be partitioned into two categories: those for which individuals should not be held responsible, and those for which they should be. We need not here be concerned with the problem of free will, and the possibility that people are not responsible for anything if they lack free will, because every society has a conception of responsibility, and we may take that as the politically salient conception. Thus, in many societies, it is thought wrong that an individual’s income be strongly correlated with her parent’s education or social position, for, assuming that that correlation reflects causality, these family characteristics seem to be ones from which children should not differentially benefit or suffer. On the other hand, most societies believe that adults should be held responsible for various choices that they make, assuming that they possess adequate information about the alternatives. Let us call the social and biological aspects of a person’s environment for which society believes he should not be responsible his _circumstances_ , those choices and actions for which he should be held responsible, his _effort_ , and the desirable good whose distribution we are concerned with the _objective._ When we have a data set that permits us to measure the inequality in the distribution of the objective, and its correlation with circumstances and effort, it is usually necessary (because data sets are finite) to choose a fairly small number of 1 This section reviews previous work of the author on the conceptualization of equality of opportunity (see Roemer (1993, 1998, 2002)).
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6 However, we are concerned with _every_ level of effort: a reasonable way of addressing all effort levels is to take the average of the numbers being maximized in (2), that is, to choose policy to I call the solution to (3) the _equal opportunity policy_ . It must be emphasized that this policy is conditional upon the definition of circumstances, and the choice of policy space<sup>2</sup> .

Define . defines an ordering on ; that is to say that: In words, is the average value of the lower envelope of the objective functions, across types.

There is a special case of interest. Typically, there are constraints that we impose upon policies, so that the policy space for the problem, , is fairly small – for example, we may limit ourselves to affine income tax policies, a uni-dimensional (small) set in the large set of income-tax policies. In this case, it may well be that there is one type – denote it type 1 -- that for all policies is unambiguously the most disadvantaged one, in the sense that its distribution function is dominated (first-order stochastically) by the others at every policy. This is virtually the case in figure 1, where the distribution functions are stacked almost unambiguously – it is obvious that the most disadvantaged 2 A generalization of program (3) is provided in Roemer (2012), where a large family of possible equality-of-opportunity measures is proposed.
7 type is the one of men whose more educated parent had fewer than twelve years of education, as its income distribution function is virtually FOSD by the distributions of the other two types<sup>3</sup> . In this case, the left-hand envelope of the distribution functions is simply the distribution function of a single type, and equation (3) reduces to: where is the average value of the objective<sup>4</sup> in the most disadvantaged type under policy φ . In this case, the equal-opportunity ethic directs us to _choose the policy to maximize the average value of the objective in the most disadvantaged type_ – assuming that this type is unambiguously the most disadvantaged, for any feasible policy<sup>5</sup> .

It is worthwhile contrasting the equal-opportunity ethic with one of its main competitors, the utilitarian ethic. Denote by the fraction of the population in type _t_ . The utilitarian policy maximizes the ordering given by: i.e., the average value of the objective in the population.

3 First-order stochastic dominance does not hold for very low incomes in figure 1; almost surely, this is the case because the children of highly educated parents are going to university, and earning very low incomes early in their careers, less than those who have entered the working-class after secondary school.

4 Recall that the area above a distribution function and bounded by the line at ordinate value one is the mean of the distribution.

5 Indeed, an alternative proposal, due to van de Gaer (1993), is to implement equality of opportunity by maximizing the function . In , the ‘min’ and ‘integral’ operators are commuted, with respect to . Fleurbaey and Peragine (2012) call an ‘ex post’ approach, and an ‘ex ante’ approach to measuring equality of opportunity. In Roemer (2012), I offer reasons for my preference for the measure . However, what the text has just pointed out is that, in special cases, the two measures coincide.
8 A third ordering, associated with John Rawls, is the ordering which maximizes the minimum value of the objective in the population; I will write: We see that the equal-opportunity ethic lies ‘between’ utilitarianism and the Rawlsian difference principle; it is less extreme than the Rawlsian formulation, in that it maximizes an _average_ of minima across effort levels. Actually, my naming of (6) as the Rawlsian view is not quite fair, for Rawls wrote that the difference principle should apply to ‘social groups,’ not individuals. If we take the different types to be the relevant social groups, then, at least in the special case where (4) holds, the equal-opportunity ethic maximizes the minimum objective value over social groups, and hence possesses a Rawlsian ancestry.

In the general case, however, if the distribution functions cross, the solution of (3) does not entail maximizing the average value of the most disadvantaged type, but rather, maximizing the area above the left-hand envelope of the distribution functions of the types, and bounded by the horizontal line of height one.

To summarize, we have provided an ordering of policies with respect to the equalopportunity ethic. That ordering takes as data a particular social view of personal responsibility, summarized in a set of circumstances and an implied typology – a partition of the population – and a policy space. The objective for which opportunities are to be equalized is typically some measurable and interpersonally comparable kind of advantage, the kind of thing a ministry in a government might be concerned with, such as income, health, life expectancy, or educational achievement.
9

# 2.   Economic development

Economic development should be measured by the extent to which a society has achieved a desirable distribution of advantage. Desirability should include considerations of both efficiency and justice or fairness. Indeed, the most common measure of economic development, GDP per capita, is based upon the utilitarian ethic, which computes the level of social welfare as the average of the utilities in the population, where utility is taken to be proportional to income.

The human development index (HDI) is not utilitarian, because it is not an average of a value of some kind of advantage over a population. But it is a convex combination of the average of three kinds of advantage over a population: the individual’s income (or consumption), his degree of literacy (which could be coded as 0 or 1), and his life expectancy<sup>6</sup> . The human development index is an average of the averages of these three dimensions over the whole society. So the HDI does not essentially depart from utilitarian practice in that it looks only at population averages, although it looks at three averages instead of only one. To be precise, this description is valid for the HDI as defined up to the 2009 Human Development Report of the UNDP. But in 2010, the Human Development Report introduced the ‘inequality adjusted human development index,’which, although still consequentialist, is not utilitarian.

Neither of these measures of development is sensitive to the distinction between circumstances and effort. They are _consequentialist_ measures of how well an economic system is doing, in that the data required to assess the system’s desirability are the values 6 An individual’s life expectancy can be defined as the average age of death of a cohort of persons with the individual’s characteristics. I am assuming that the life expectancy in a country is the average of life expectancies of individuals, so defined.
10 of various outcomes for members of the population. The equal-opportunity view, however, focuses upon the distinction between circumstances and effort. Thus, to assess the desirability of a system, it requires not only the data just mentioned, but also knowledge of the _type_ of each individual. It is a non-consequentialist measure, for it will assess differently the same outcome for two individuals, if they have different circumstances. Utilitarianism condemns inequalities if their elimination would increase average or total welfare (however it is measured); opportunity egalitarianism condemns them to the extent they are due to circumstances beyond the control of the individuals concerned. The views are quite different.

Opportunity egalitarianism is not only a superior ethic to utilitarianism, it is the one implicitly endorsed by members of many societies. Suppose one asks the proverbial man on the street, “Do you think that the inequality between the rich Mr. _A_ and poor Ms. _B_ is unjustified?” it is unlikely that he will answer, “Only if a redistribution from _A_ to _B_ would increase their total welfare.” But he might well answer, “It depends upon how hard they each worked.” In other words, the popular views of justice are not consequentialist, they are based upon notions of _desert,_ and desert is based upon measurements of effort. Our man on the street must know more than the aggregate distribution of the objective to assess whether that distribution is fair – he must know the (disaggregated) distributions of the objective by type. The source of the inequality matters, ethically speaking, but these sources are ignored by looking only at outcomes<sup>7</sup> .

7 There is substantial survey and experimental work which examines the views that people in various societies have concerning distributive justice. An extensive discussion of this literature is found in Gaertner and Schokkaert (2012).
11 We cannot maintain that the most common measures of economic development are value free: they are derived from a utilitarian ethic. To this claim one might object that the measure of GDP per capita has nothing to do with utilitarianism, it is simply a proxy for technological development. But this cannot be right, because economists are not interested in technological prowess per se: we are interested in human welfare. We would not consider a society highly developed which possessed a fine technology run by slaves, whose product all went, but for the slaves’ subsistence, to the prince. So an attempt to justify the GDP per capita measure of development as a value-free measure of technological accomplishment has the undesirable consequence of obliterating the distinction between economics and engineering – namely, that economics must always focus upon human welfare<sup>8</sup> .

Therefore, we should use the best conception of justice or social welfare to derive a measure of economic development. Perhaps the extent to which opportunities have been equalized is not the best such conception, but it dominates, so I believe, utilitarian measures. It is better to measure the level of economic development by some statistic that reflects equality of opportunity rather than by a utilitarian measure.

But what version of equality of opportunity should we use to evaluate economic development in a panel of countries? What should be the circumstances and the objective? To be most similar to GDP per capita, the objective should be income – let us say, post-fisc income including the per capita value of public goods. Begin with circumstances that include the educational level and occupations of the parents of the 8 I do not wish to denigrate the goals of engineers. However, there is a sense in which engineers are interested in technological efficiency as a goal, while economists are interested in it only insofar as technological efficiency is necessary for Pareto efficiency (in which the goal is human welfare).
12 individuals, and the ethnicity and gender of the individual<sup>9</sup> . Then calculate the number , where is the status quo policy. This is the first component of the two-dimensional measure of economic development that I propose. The value is the average income of those in society who are most disadvantaged by circumstances. Choosing it as a measure of economic development is inspired by the view, attributed to Mohandes Ghandi, among many others, that “a nation’s greatness is measured by how it treats its weakest members.<sup>10</sup> ” This proposal is not new. Indeed Bourguignon, Ferrera and Walton (2007) propose a dynamic and closely related version of : namely they say that the present discounted value of the average income of the most disadvantaged type should be maximized for development policy to be equitable.

# 3.  The <u>degree of opportunity equality</u>

I have proposed to measure the _level of development_ of a society as the value of the equal-opportunity social welfare function. Of course, we are highly restricted in our ability to measure economic development when we must use a single number to capture it. In particular, applying the measure defined in (4) to income does not allow us to distinguish the _wealth_ of the society from the _degree_ to which the society has succeeded in eliminating injustice – that being the influence of circumstances upon inequality. To do this, I propose a second measure, which I call the _degree of opportunity equality_<sup>_11_</sup> _._ 9 How one treats gender depends upon whether one uses households or the individual as the unit.

10 The quotation is ubiquitously attributed to Ghandi, over the original statement of it is obscure.

11 Again, this proposal is not new. It is a special case of the ‘inequality of opportunity ratio (IOR)’ defined in Ferreira and Gignoux (2011). Ferreira and Gignoux’s preferred measure of inequality is not CV<sup>2</sup> but the ‘mean logarithmic deviation.’ The same idea for measuring the degree of inequality due to circumstances is proposed in Checchi and Peragine (2010) as well.
13 A society will have achieved equality of opportunity to the extent that the contribution of differential circumstances to total inequality in the distribution of the objective is small. Let the distribution function of the objective in a given society be _H,_ and the distribution functions of the objectives in the types be ; then Suppose we measure inequality in a distribution by the coefficient of variation squared (CV<sup>2</sup> ), that is: where the mean of _H_ is . Denote the mean of . Without loss of generality, suppose that we have enumerated types so that is a monotone increasing sequence.

Define the distribution: Clearly the mean of is . If were the actual distribution of the objective in society, then everybody in a given type would have exactly the same value of the objective, equal to the mean of the objective in that type. Were this the case, then the contribution of effort to inequality would be nil, as no variation of accomplishment would exist within any type. Now it is well-known that we can decompose as follows:
14 where . Since both contributions in this decomposition are positive, it is natural to interpret as the amount of inequality due to circumstances, and the amount of inequality due to effort. I therefore propose, as a measure of the _degree_ of opportunity equalization, the index: We may want to think of as an upper bound on the fraction of inequality due to effort because surely some circumstances have not been taken into account, whose effect is measured, residually, as ‘effort.’ My suggestion is that we measure economic development by the ordered pair . Note that neither component of _d_ is a consequentialist measure. One cannot recover either or η from knowledge of the distribution of income (more generally, the objective) alone. One must know, as well, the circumstances of individuals, which capture the concept of responsibility salient for the society in question.

# 4.  Country calculations of the <u>level and degree of development</u>

In this section, I calculate the value of _d_ for a set of OECD countries. The data upon which these calculations are based are taken from EU-SILC 2005. The sample consists of male workers, who are partitioned into three types, based upon the maximum of the worker’s parents’ educational levels: <u>Type 1: the worker’s more educated parent had at most lower secondary</u> education
15 <u>Type 2: the worker’s more educated parent had at least upper secondary education</u> but not tertiary education <u>Type 3: the worker’s more educated parent had at least some tertiary education.</u> The net income for each respondent is recorded, which includes earnings, selfemployment income, after taxes and transfers. The _single characteristic_ of type in these calculations is parental education which takes on three values.<sup>12</sup> The fact that income does not include the value of public goods is a weakness of the measure. If a country has a high rate of taxation, and a substantial fraction of tax revenues finance public goods (as opposed to transfer payments), this will not be reflected in the income data. Transfer payments are included in the definition of income.

Figure 1 presents the income-distribution functions for Austria, by type, which is in many ways typical. Since the left-hand envelope of the three CDFs is, for all practical purposes, the CDF of type 1, the level of development is simply the mean of type 1’s income. For Austria, the level and degree of development, as defined in the previous section, are: .

(Incomes are measured in Euros.) It may surprise the reader that only about 3% of income inequality is attributed to circumstances, but this is quite typical for advanced European countries, given that only one circumstance is specified. For Latin American 12 I am grateful to Daniele Checchi and Francesco Scervini for providing me with the data set. For an exact description of the data set, see Checchi, Peragine, and Serlenga (2010). The computation of the degrees of development and the type-distributions of income were performed by the author using _Mathematica_ ; I will supply the code upon request.
16 countries, this number will be considerably larger. Indeed, Ferreira and Gignoux (2011), in their table 8, present their comparable measure to , using the mean logartithmic deviation of income as the inequality measure, for a set of six Latin American countries. Their set of circumstances is denser than mine. For some countries (Guatamala), the degree of inequality attributable to circumstances is over 50%.

Figure 2 presents the income CDFs of the three types for one of the least developed countries in sample, Hungary, and for one of the most developed, Denmark.

We see that the inter-type dispersion is considerably more dramatic in Hungary than in Austria, while the CDFs in Denmark are very close together. The graphs of the three CDFs for the other countries in the sample are presented in an online appendix.

Figure 3 plots the ordered pairs for all 22 countries in the sample<sup>13</sup> . Some comments:

1.  The eastern European countries are the worst off with respect to the index : these comprise Lithuania (LT), Estonia (EE), the Czech Republic(CZ), Poland (PL),  Latvia (LV), and Hungary (HU).    (Slovenia (SI) does somewhat better.)  But Spain (ES) is also very low on this measure.  With respect to the degree of development, η , the eastern European countries span a range from about 92% to 99.5% .

2. Greece appears to do very well on the degree of development: I question whether the data are reliable.

> 13 EU-SILC also contains data for Cyprus, but there are so few observations that I do not consider the CDFs to be meaningful. I excluded as well Ireland from the sample, because I believe the data have been miscoded: according to the data, the middle type in Ireland is worse off than the most disadvantaged type.
17 3. We may define a partial order with respect to development; a country _j dominates_ a country _k_ if With regard to this partial order, no country in the sample dominates all others. Thus, we can say there exists no most developed European country. Conversely, however, there are five countries that are undominated by any other: Denmark (DK) , Iceland (IS), Germany (DE), the UK, and the Netherlands (NL). These data are from 2005, and doubtless Iceland, post-crash, no longer enjoys this status.

Table 1 presents the same data as figure 1.

As noted, Ferreira and Gignoux (2011) calculate a similar statistic to for six Latin American countries. Their calculation differs from the one presented here using the SILC data in two ways: they have a different set of circumstances, and they use a different measure of inequality. I have calculated an index for Brazil, using a data set which reports income of workers for a typology whose circumstances are race, gender of the head of household in which the worker was raised, and urban-rural<sup>14</sup> . There are four races: white, mixed, black, and ‘other’ – thus 16 types. I limited my analysis to nine types, which comprise 94.5% of the sample, not including the four types of ‘other’ race, or the three rural types with female head-of-household parent. For this population, we compute , which is surprisingly high – only 1.6% of income inequality is attributed to these circumstances. This contrasts with the IOR computation of Ferreira and Gignoux (2011), in which, in Brazil, about 32% of inequality is due to 14 I thank Sean Higgens for providing me with the Brazilian data, which were collected as part of the Commitment to Equity project. See Higgens and Pereira (in press) for details.
18 (their) circumstances, which are {ethnicity, father in agriculture, father’s education, mother’s education, birth region}. Surely the inclusion of parental education in the Ferreira-Gignoux data set increases the role of circumstances in generating inequality.

Figure 4a presents the distribution functions of disposable income for the Brazilian types (white, male household head, urban), (white, female household head, urban), (white, male household head, rural) in order of stochastic dominance (using the Higgens-Pereira data set). Thus, it appears that one has better opportunities if one is raised by a woman in the city than by a man in the countryside. Figure 4b presents the analogous three distribution functions for the mixed race. The order of stochastic dominance is the same as in figure 4a. Figure 4c places these two plots together: we see that even the _most disadvantaged_ white type first-order-stochastic-dominates the _most advantaged_ mixed type.

It turns out that the three black types also have distribution functions ordered in the same way. Figure 5 presents the distribution functions of the black types (in violet) superimposed upon figure 4c. We observe that the first two black types ((male household head, urban) and (female household head, urban)) have distribution functions that are virtually coincident with the analogous mixed types, and the distribution function of (black, male household head, rural) appears to FOSD the comparable ‘mixed’ type. Indeed, the distribution function of the (black, male household head, urban) type is virtually invisible in figure 5, as it coincides so closely with that of the (mixed, male household head, urban) type. The conclusion appears to be that there is racial discrimination in Brazil which favors whites over non-whites, but there is no special
19 discrimination against black workers, who appear, if anything, to have somewhat better opportunities than ‘mixed’ workers.

Finally, Björklund, Jäntti and Roemer (2012) study income in Sweden, using a large data set that permits the partition of the population into over 1100 types, based on six circumstances, each partitioned into several levels. Using methods different from the ones discussed here, they conclude that at least 25% of income inequality is due to circumstances<sup>15</sup> . Contrast this to the 1.5% figure for Sweden from table 1.

# 5.  Equity ‘versus’ development<sup><u>16</u></sup>

It is often said that equity and efficiency are competing goals -- that equity is purchased at the expense of efficiency. There are two senses in which this phrase may be uttered. The first is that redistributive taxation may be purchased only at the cost of Pareto inefficiency, due to workers’ and firms’ facing different effective wages. The second sense is that redistribution may lower total output. These two claims are in principle independent. There may be policies which re-allocate income in a more equitable manner, lower total output, but are not Pareto inefficient. (Think, for example, of re-allocating educational funds from tertiary education to secondary education in a poor country. This might have a purely redistributive effect, without significant consequences for Pareto efficiency.) I wish to criticize the second usage of the phrase. Saying that there may be a trade-off between equity and efficiency _where efficiency is measured as total output_ is equivalent to saying there is a trade-off between equity and the utilitarian measure of 15 Perhaps, most critically, IQ in adolescence is taken as a circumstance.

16 The point in this section is discussed more extensively in Roemer (2006).
20 development, which (in its simplest form) is given by output per person. In fact, both the measures of equity that I have proposed in the ordered pair _d_ , and output per capita, are measures of equity according to different normative criteria, as discussed in section 2. Indeed, because utilitarianism was the reigning conception of distributive justice until at least the 1970s, it is unsurprising that GDP per capita was the corollary measure of development in economics.

There is an increasing number of economists who argue that ‘improving equity improves efficiency.’ (The World Development Report (2006) presses this point, but the argument goes back many years.) My objection is not to the substantive claim, that equalizing opportunities often increases productivity and national income, but only to the tradition of assigning utilitarianism _primus inter pares_ as the normative view which _defines_ efficiency.

If the view of economic development I here advocate is adopted, there may be a significant change in policy evaluation. One would not have to justify investment in very disadvantaged social groups by showing that such investment increased total output. In the long run, such a conflict might not exist: but often, policy makers must evaluate the consequences of their policy choices in the short run. If a country is evaluated on the basis of its ordered-pair statistic rather than on GDP per capita, policies could be quite different.

# 6.  A World-Bank proposal for measuring equal opportunity

The World Bank has been an important innovator in bringing considerations of equal opportunity into economic development. Its two important publications, to date,
21 have been the 2006 World Development Report, _Equity and Development,_ and a monograph, _Measuring inequality of opportunities in Latin America and the Caribbean_ (Paes de Barros et al., 2009). The more recent publication contains a wealth of information on the effects of social circumstances on various measures of achievement and output.

Paes de Barros et al. (2009) propose a measure of equality of opportunity.

Consider a particular kind of opportunity, such as ‘attaining the sixth grade in elementary school.’ Let the total sixth-grade attendance in a country be _H_ , and the total number of children of sixth-grade age be _N_ , and define to be the _access_ on average of children to the opportunity of a sixth-grade education. measures the level of this opportunity in the country, but not the extent to which access is unequal to different children, based upon their social circumstances. Now using a logit model, estimate the probability that each child, _j_ , in the country has of attending the sixth grade, where that probability is a function of a vector of circumstances; denote this estimated probability by . Define . _D_ measures the variation in access to the opportunity in question across children in the country. The normalization guarantees that . Now define the _human opportunity index_ as ; note that .

The human opportunity index is a non-consequentialist measure of development, because the probabilities can only be computed knowing the circumstances of the children. The measure combines a concern with the level of provision of opportunities
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23 Despite the fact that effort is not explicitly mentioned in defining the index, effort is reflected in measure, because the distributions appear in the calculation. Indeed, the first term measures the level of opportunity in the country, while the second term is a penalty for the degree to which this opportunity is mal-distributed with respect to circumstances (e.g., if there were no inequality of opportunity, then for all _t,_ and the penalty is zero).

In expression (12), the first term on the right-hand side, , plays the role that plays in my measure: it measures the level of development. But while focuses upon how well off the most disadvantaged type is doing, is a level for the society at large. The second component of my measure, η , is explicitly derived to show the degree to which inequality is due to circumstances, while the second term on the right-hand side of (12) is a form of a variance. Certainly these two measures are getting at the same phenomenon. I have a slight preference for my proposal, as it is more carefully justified as measuring what we are concerned with. But these are minor criticisms; certainly, the measure _O_ is in the spirit of thinking of economic development as opportunity equalization.

# 7.  Conclusion

Inequality has become an important focus in development economics in recent years, and this is a step forward from the days when only GDP per capita was considered to be salient. But an important weakness in the entry of inequality into the field has been treating all inequality as having the same ethical status. This is seen in the very large literature on the measurement of inequality, where the concern has been upon whether the
24 statistical properties of various inequality measures conform to our intuitions concerning when equality is _large or small_ . These discussions ignore the issue of whether inequality is _innocuous or undesirable_ – that is, the ethical status of the inequality. The equalopportunity literature introduced the latter distinction into economic theory, and it built on the introduction of the issue of responsibility into egalitarian political philosophy, through the writings of R. Dworkin (1981a,b), G.A. Cohen (1989) and R. Arneson (1989). For discussions of this literature, from economists’ viewpoints, see Roemer (1996, 2009) and the treatment of Fleurbaey (2008).

It is useful to further compare the equal-opportunity approach to inequality to the approach represented by the human development index, based upon the work of Amartya Sen on functionings and capability. As is well known, Sen’s (1980) major point was that there are objective measures of human functioning that are important for any conception of welfare, and the set of vectors of functionings, available to a person, which Sen defined as her _capability,_ is a measure of the opportunities that she has. Sen’s intervention was post-Rawls and pre-Dworkin: his main foil was Rawls’s choice of primary goods as the equalisandum, which he proposed replacing with capabilities; and his conception of responsibility was implicit in the idea that, if capabilities, so defined, were ‘equal’ (whatever that should mean) across persons, then if individuals chose different vectors of functioning from these sets, the result was of no ethical consequence. The treatment of responsibility, in Dworkin (1981,1982), was significantly more explicit, and led to the equal-opportunity literature.

The proposal I have stated here, and the human development index (HDI), are complementary. The HDI broadens the objective of concern from income (GDP) to a
25 set of functionings, but continues to average over the population as a whole, and ignores the source of inequality<sup>18</sup> . The equal-opportunity approach – as I have advocated applying it to a set countries – retains income as the objective, but disaggregates the population into types based upon circumstances that are beyond the control of individuals. The HDI approach says that human accomplishment along dimensions other than income is important, and the equal-opportunity approach says that inequality is bad only if it is of a certain kind.

Of course, it is possible to unite the two approaches. Instead of using income as the measure in my proposal, one could measure human development _disaggregated by types_ , where type continues to be defined according to a set of circumstances, and then the two-dimensional index _d_ would allow us to assess levels and degrees of development with regard to the various Sen-inspired functionings. It would be ideal to have data sets that permitted us to do this. The reason I have here proposed using only income is that I think, at this point, we do not have the data to compute the distribution of levels of human development by type for a large set of countries. However, the recent publication of the results of the Global Burden of Disease project ( see the entire issue of _The Lancet,_ December 13, 2012) indicates that this lacuna may be filled, as we may soon have available distributions of longevity by country and by type<sup>19</sup> .

Note that the issue of the ethical status of inequality is quite different from another way that inequality can be good or bad, and that is, with regard to its effect on 18 In the 2011 Human Development Report, the human development index is calculated by taking a geometric mean of national income, literacy, and longevity, rather than a convex combination of them.

> 19 In this issue of _Lancet_ , longevity and morbidity figures are given for almost all countries in the world.   Information on these measures of welfare by type is not, however, reported.
26 incentives. Bad inequality in this sense – inequality that is bad for incentives – will be condemned by the utilitarian measure of GDP per capita, because its elimination will increase social output. This is to be distinguished from inequality that is bad because it reflects disadvantage due to circumstances: as I have emphasized, eliminating this kind of inequality is not -- at least in the short run – synonymous with increasing total output or welfare.

The equal-opportunity approach, which focuses upon eliminating inequalities that are due to circumstances for which persons should not be held responsible, is both good ethics and also good policy – by which I mean it is policy supported by the majority of people in many countries. For we know from survey data that, globally, people believe injustice occurs when low incomes are due to bad luck as opposed to low effort. What differs across countries is the extent to which citizens attribute low incomes to bad luck as opposed to low effort: in Brazil, a much larger fraction believe poverty is due to bad luck than in the United States (and perhaps this reflects reality). Indeed, the popular moniker associated with equality of opportunity – it levels the playing field -- can be interpreted as a way of saying that disadvantages that some face due to circumstances beyond their control should be eliminated before the competition for economic goods begins.