Inequality and Fairness

This study uses John Rawls’ behind-the-veil of ignorance device as a fairness criterion to evaluate social policies and applies it to a contracting model in which the terms equality of opportunity and equality of result are well defined. The results suggest that fairness and inequality—even extreme inequality—are compatible. In a static world, when incentives must be provided, fairness implies equality of opportunity, but inequality of result. In a dynamic world of long-lived individuals, fairness implies not only inequality of result, but also, eventually, infinite inequality of result. If each period of the dynamic model is interpreted as a generation, then eventual infinite inequality holds for opportunity as well, as long as fairness is from the perspective of the first generation. If preferences of later generations are taken into account, then inequality of opportunity still occurs, although not at extreme levels. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. While conceding that normative issues like fairness or justice may be appropriate considerations when discussing social policies informally, economists have a strong tradition of shying away from such considerations when they evaluate policies formally. Instead, economists traditionally see their expertise as in objectively evaluating whether a social policy is efficient. Perhaps the best illustration of this tendency to avoid normative issues is the familiar Edgeworth box diagram. In an endowment economy with two goods and two agents, efficiency implies that each agent’s marginal rate of substitution between the two goods must equal the other agent’s. If both agents like both goods, then this equality can occur when the allocation of the goods is quite unequal, such as when either agent has almost all of the aggregate endowment of both goods. Economists tend to be willing to criticize allocations in which marginal rates of substitution are not equated (since then both agents can be made better off by an allocation in which these rates are equated). But economists tend to be unwilling, at least formally, to choose among the many efficient allocations. Nevertheless, starting with the work of Edward Green (1987), economists have developed a large literature on dynamic contracting theory which has implications for inequality of consumption across households and, I argue, on whether such inequality is fair. In that literature, society faces a trade-off between insurance and incentives, and inequality results as the product of efficient mechanisms intended to induce good behavior. I argue here that the efficiency notion of these studies corresponds closely (but not perfectly) to the fairness notion of political philosopher John Rawls (1971). If my argument is accepted, then dynamic contracting theory has something to say about fairness as well as efficiency. It says that fairness and inequality are not incompatible: a fair allocation can imply inequality. But more surprisingly, the theory says that a fair allocation can imply extreme inequality of both opportunity and result. To make this argument, I present a model which allows the consideration of equality of opportunity and result. The model economy has a fixed amount of land that is a necessary input to household production; that is, a household with little or no land has little or no opportunity to produce. Thus, in the model, one household having more land than another implies inequality of opportunity while one household having more consumption than another implies inequality of result. This fixed amount of land is also useful for deriving my most extreme conclusion: in the fair allocation, incentive issues cause the land allocation of almost all households to converge to zero, implying eventual infinite inequality of both opportunity and result. Rawls’ Fairness vs. Economists’ Efficiency To get to that extreme conclusion, I must establish a connection between Rawls’ notion of fairness and economists’ notion of efficiency in models of dynamic contracting. Rawls’ notion of fairness generally corresponds to economists’ notion of ex ante efficiency. To see this, consider a world in which, by pure luck, some are born with valuable skills (the skilled) and some, with less valuable skills (the unskilled). Again, in evaluating alternative social policies, economists tend to avoid considering what is the best transfer from the skilled to the unskilled because that involves making a value judgment: best from whose perspective? Instead, economists tend to evaluate social policies in terms of ex post efficiency. Economists are willing to call social policy A “inferior to” social policy B if both the skilled and the unskilled weakly prefer social policy B (and at least one group strictly prefers policy B). But economists are traditionally silent on the ranking of these policies if one group prefers policy A and the other, policy B (as is true if policy A is a transfer from the skilled to the unskilled and policy B, a zero transfer). Rawls (1971), however, is quite willing to consider the best transfer from the skilled to the unskilled. His method is to step back behind “a veil of ignorance” to a world in which everyone knows the two groups will exist, but no one knows which group anyone will be in. By definition, many things may be uncertain from behind the veil, but everyone is in the same informational position. In such a world, there is no question of “best from whose perspective?” There is only one perspective—that of individuals who see all possible outcomes as possibly happening to them. This common perspective, then, gives a way to rank social policies that economists are traditionally loathe to rank. Social policy A is better than social policy B if and only if it is better from the behind-the-veil perspective, and the best social policy is the one that maximizes welfare from that perspective. Still, in some types of economic problems, notably, those involving insurance, Rawls’ notion of fairness corresponds to the economist’s notion of ex ante efficiency. Economists have little reticence about arguing that when households pool risk regarding home fires and as a result transfers go from households which do not have fires to households which do, this is efficient risk-sharing. In reality, people actually do make insurance contracts before they know which group they are going to be in. Formally, Rawls’ criterion amounts to simply pretending that the skilled vs. unskilled scenario (in which everyone knows which group they are in) is the same as the fire vs. no fire scenario (in which no one knows, at the point of contracting, which group they are in) and choosing the transfer from the skilled to the unskilled to correspond with the efficient insurance arrangement that people would have chosen if they had had an opportunity to choose. I depart here from Rawls’ notion of fairness regarding the preferences of those behind the veil. I assume that preferences regarding risk and time are the same for those in the world and those behind the veil and take forms commonly assumed by economists. Rawls argues that individuals behind the veil will be more risk averse than individuals observed in the world and will not discount the future. (In fact, Rawls argues that behind the veil, individuals will be infinitely risk averse, or care only about maximizing welfare in their own worst-case scenario.) This is how Rawls (1971, pp. 152ff) derives his familiar maximin criterion: policy A is preferred to policy B from behind the veil if and only if the welfare of the worst outcome for any individual under policy A exceeds the welfare of the worst outcome under policy B. Here, I show that if more reasonable levels of risk aversion and some discounting are allowed, then what is chosen from behind the veil can change drastically. A Static Model I start by considering a simple contracting model, an economy with only one time period. Even in this simple model, we shall see that fairness implies some inequality. This economy has a continuum of identical households and a single divisible unit of land. The single consumption good c is produced by households using land not allocated to private use. Specifically, if z is the household’s land allocation and θ ∈ {0,θ̄} is the fraction of the household’s land allocated to production of the consumption good, then the household’s production is