Pareto Efficiency and Identity∗

This paper examines the set of Pareto efficient allocations in a finite period Mirrlees (1971, 1976) economy; each period represents a lifetime for an agent who cares about the utility of his descendants. In making Pareto comparisons, we use an interim concept of efficiency, and consider an individual as indexed not only by his date of birth but also by the history of events up to his birth, including his own type. That is, we assume the child of a high skilled parent is a different person than the child of a low skilled parent, even if both children have the same skill level. Our contributions are characterization of these efficient allocations and their implementation. We completely characterize the set of efficient allocations under full information. We show that for efficient allocations, implicit inheritance taxes from the perspective of the parent’s type, can be either progressive or regressive. Further, imposing no taxes of any kind, coupled with each agent owning his own production, results in a Pareto efficient allocation. Under private information, we completely characterize the set of Pareto efficient allocations for the two-period economy where skill types take on two values, and again show that implicit inheritance taxes can be either progressive or regressive, again relative to the parent’s type. For more general multi-period economies with private information, we show that the reciprocal Euler condition of Rogerson (1985) and Golosov, Kocherlakota, and Tsyvinski (2003) holds as a necessary condition, but as an inequality and that the expected value of implicit inheritance tax rates conditional on a parent’s history are weakly negative. Finally, we derive conditions such that given private information, no taxes of any kind, coupled with each agent owning his own production, results in a Pareto efficient allocation. ∗Christopher Phelan: Department of Economics, University of Minnesota, Federal Reserve Bank of Minneapolis, NBER. Aldo Rustichini: Department of Economics, University of Minnesota. We thank Larry Jones, Manuel Amador, Fernando Alvarez, Hector Chade, Tom Phelan, Chris Sleet, Sevin Yeltekin and workshop participants at Stanford University, the Minnesota Workshop in Macroeconomic Theory, the Federal Reserve Bank of Philadelphia, Arizona State University, and Carnegie-Mellon University for useful discussions. We thank the editor and the referees for helpful comments, especially those that inspired sections 3.3 and 4.4. Aldo Rustichini thanks the National Science Foundation (grant SES-1061817). The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.