Inequality , Social Discounting and Progressive Estate Taxation ∗

To what degree should societies allow inequality to be inherited? What role should estate taxation play in shaping the intergenerational transmission of welfare? We explore these questions by modeling altruistically-linked individuals who experience privately observed taste or productivity shocks. Our positive economy is identical to models with infinite-lived individuals where efficiency requires immiseration: inequality grows without bound and everyone’s consumption converges to zero. However, under an intergenerational interpretation, previous work only characterizes a particular set of Pareto-efficient allocations: those that value only the initial generation’s welfare. We study other efficient allocations where the social welfare criterion values future generations directly, placing a positive weight on their welfare so that the effective social discount rate is lower than the private one. For any such difference in social and private discounting we find that consumption exhibits mean-reversion and that a steadystate, cross-sectional distribution for consumption and welfare exists, where no one is trapped at misery. The optimal allocation can then be implemented by a combination of income and estate taxation. We find that the optimal estate tax is progressive: fortunate parents face higher average marginal tax rates on their bequests. Introduction Societies inevitably choose the inheritability of inequality. Some balance between equality of opportunity for newborns and incentives for altruistic parents is struck. We explore how this balancing act plays out to determine long-run inequality and draw some novel implications for optimal estate taxation. ∗ For useful discussions and comments we thank Daron Acemoglu, Fernando Alvarez, George-Marios Angeletos, Abhijit Banerjee, Gary Becker, Bruno Biais, Olivier Blanchard, Ricardo Caballero, Dean Corbae, Mikhail Golosov, Bengt Holmstrom, Chad Jones, Narayana Kocherlakota, Robert Lucas, Casey Mulligan, Roger Myerson, Chris Phelan, Thomas Philippon, Gilles Saint-Paul, Rob Shimer, Nancy Stokey, Jean Tirole and seminar and conference participants at the University of Chicago, University of Iowa, The Federal Reserve Bank of Minneapolis, MIT, Northwestern, New York University, IDEI (Toulouse), Stanford Institute for Theoretical Economics (SITE), Society of Economic Dynamics (SED) at Budapest, Minnesota Workshop in Macroeconomic Theory, NBER Summer Institute and the Texas Monetary Conference held at the University of Austin in honor of the late Scott Freeman. This work begun sparked by a seminar presentation by Chris Phelan at MIT in May 2004. We also gained insight from a manuscript by Scott Freeman and Michael Sadler that Dean Corbae brought to our attention. 1 Existing normative models of inequality reach an extreme conclusion: inequality should be perfectly inheritable and rise steadily without bound, with everyone converging to absolute misery and a vanishing lucky fraction to bliss. This immiseration result is robust; requires very weak assumptions on preferences (Phelan, 1998); and obtains invariably in partial equilibrium (Green, 1987; Thomas and Worrall, 1990), in general equilibrium (Atkeson and Lucas, 1992), and across environments with moral-hazard regarding work effort or with private information regarding preferences or productivity (Aiyagari and Alvarez, 1995). We depart minimally from these contributions, adopting the same positive economic models, but a slightly different normative criterion. In a generational context, previous work with infinitelived agents characterizes the instance where future generations are not considered directly, but only indirectly through the altruism of earlier ones. On the opposite side of the spectrum, Phelan (2005) proposes a social planner with equal weights on all future generations. Our interest here is in exploring a class of Pareto-efficient allocations that take into account the current population along with unborn future generations. We place a positive and vanishing Pareto weight on the expected utility of future generations, this leads effectively to a social discount rate that is lower than the private one. This relatively small change produces a drastically different result: long-run inequality remains bounded, a steady-state, cross-sectional distribution exists for consumption and welfare, social mobility is possible and everyone avoids misery. Indeed, welfare typically remains above an endogenous lower bound that is strictly better than misery. This outcome holds however small the difference between social and private discounting, and regardless of whether the source of asymmetric information is privately observed preferences or productivity shocks. We begin by modeling a positive economy that is identical to the taste-shock setup developed by Atkeson and Lucas (1992). Each generation is composed of a continuum of individuals who live for one period and are altruistic towards a single descendant. There is a constant aggregate endowment of the only consumption good in each period. Individuals are ex-ante identical, but experience idiosyncratic shocks to preferences that are only privately observed—thus ruling out firstbest allocations. Feasible allocations must be incentive compatible and must satisfy the aggregate resource constraint in all periods. When only the welfare of the first generation is considered, the planning problem is equivalent to that of an economy with infinite-lived individuals. Intuitively, immiseration then results from the desire to smooth the dynastic consumption path: rewards and punishments, required for incentives, are best delivered permanently. As a result, the consumption process inherits a random-walk component that leads cross-sectional inequality to grow endlessly without bound. Infinite spreading of the distribution is consistent with a constant aggregate endowment only if everyone’s consumpMany find the immiseration result perplexing and some even find it morally questionable, but it is also inconvenient from a practical standpoint. Long-run steady-states often provide a natural benchmark to study dynamic economies, but such long-run analyses are not possible for private-information economies without a steady-state distribution with positive consumption. This has impaired the study of long-run implications of optimal taxation, so common in the Ramsey taxation literature.