PARENTS, CHILDREN, AND LUCK: EQUALITY OF OPPORTUNITY AND EQUALITY OF OUTCOME
This paper considers three perspectives on parents, children and luck (PCL) each with a venerable pedigree. The first perspective focuses on the intergenerational elasticity (IGE) of income transmission. Within this perspective, the older literature traces the consequences of higher or lower IGE for the evolution of inequality of income. The more recent literature, on "The Great Gatsby Curve" sees the causality running the other way, from current inequality to IGE. The second tradition (PCL II) approaches intergenerational mobility through transition matrices and sets out views on "greater mobility" through this lens. But these views are not necessarily consistent with each other, and a social welfare function approach is needed to pronounce on comparisons between societies. Taking a dynastic inequality approach, Kanbur and Stiglitz (2015) show that "equality of opportunity" a transition matrix with identical rows does not necessarily lead to lower dynastic inequality than all other transition matrices. Finally, the third perspective on parents, children and luck (PCL III) is presented by Roemer (1998) and in particular by applications of the framework to quantify "inequality of opportunity" It is argued here that these approaches have serious empirical and conceptual flaws, and may understate the true degree of inequality of opportunity. Paper written for Festschrift for Joseph Stiglitz, to celebrate his fifty years as a teacher. It is based on based on a presentation at "A Just Society: A Conference in Honor of Joseph Stiglitz" at Columbia Business School, October 16 17, 2015. Joe and I started discussing these issues in 1976, when he came to Oxford as Drummond Professor and I became his student. We have continued our discussions over the past four decades, and I look forward to them in the years to come. 4 1. Motherhood and Apple Pie Who could possibly be against equality of opportunity, especially when compared to equality of outcomes? Not, it would seem, many egalitarian thinkers, for whom "the development of egalitarian theory, since Rawls, may be characterized as an effort to replace equality of outcomes with equality of opportunities, where opportunities are interpreted in various ways. Metaphors associated with this view are "leveling the playing field," and "starting gate equality" Wagstaff and Kanbur (2015) call equality of opportunity the new motherhood and apple pie in policy discourse. There are many translations of this metaphor into concrete specifications. Roemer (1998) following Dworkin (1981a,b) and others, famously distinguishes between "circumstances" and "effort" as characterizing those factors which are respectively outside and within the control of the individual in determining outcomes. Equality of opportunity is then equalization of the impact of circumstances on outcome, without touching the difference in outcome induced by effort. There are many possible types of circumstance, but two stand out in the literature. First, characteristics of parents, over which presumably children have no control. Second, "brute luck" to use Dworkin's phrase, in other words random events over which the individual has had no influence over. There are other circumstances such as gender or ethnicity, although the latter could equally well be treated as the consequence of parental characteristics. Leaving to one side complex questions on the social construction of categories, gender is outside the control of an individual at birth, depending on parental genetic characteristics combined with the random processes of chromosomal crossover in reproduction. But then so, presumably, are all of the genetic traits that go under the label of "talent." Pushed to the limit, this chain of reasoning would leave very little outside of the realm of circumstance. But in a narrower economic setting, let us think of the circumstances of a child as being parental income, and let us describe economic processes as leading to a stochastic outcome for the child, conditional on parent's income. This simple formulation leads to a stochastic process through which the income distribution evolves over time, depending on the conditional distribution of the child's income given parent's income. The tightness of the conditioning can be thought of as a measure of the "inequality of opportunity," and naturally leads to the question of whether greater inequality of opportunity leads to greater inequality of outcome, and vice versa. It is these interactions between parents, children and luck (PCL) in the determination of the equality of opportunity and equality of outcome which are reviewed and explored in this paper. Section 2 begins with the simplest well known setting in which parental income determines child income but with shocks. The implications for long run income distribution of different degrees of mobility are traced out. Section 3 takes up an alternative tradition in the literature on the measurement of intergenerational mobility, based on transition matrices, and asks how common views on "greater mobility" match perspectives on dynastic inequality. Section 4 returns to the recent literature inspired by Roemer (1998) and presents a brief critique. Section 5 concludes.