Wharton Pension Research Council Working Papers

Document Type

Working Paper

Date of this Version



Security markets between generations are naturally incomplete in a laissez-faire economy since risk sharing agreements cannot be made with the unborn. But suppose that generations could trade if, for example, a representative of the unborn negotiated on their behalf today. What would the trades look like? Can government fiscal policy be used to replicate these trades? Would completing this missing market be Pareto improving when the introduction of the new security changes the prices of existing assets? This paper characterizes analytically the hypothetical trades between generations and shows how the government can replicate these trades by taxing the realized equity premium on investments in a symmetric fashion. This tax is equivalent to the government providing a “collar-like” guarantee on personal investments. When technology shocks are mostly driven by changes in depreciation, a positive tax (a long collar) replicates the hypothetical trades; this tax is also Pareto improving under fairly general conditions. When technology shocks are mostly driven by changes in productivity, the choice between a positive and negative tax rate is unclear. However, with log utility, Cobb-Douglas production, and a depreciation rate less than 100 percent, a negative tax (short collar) is Pareto improving. Simulation analysis is used to consider more complicated cases, including when depreciation and productivity are both uncertain. Under the baseline calibration for the U.S., a positive tax (a long collar) on the equity premium is Pareto improving.


Social Security, Trust, Pension, System, Countries, Workers, Private, Reform, Demographic, Model

JEL Code

H0, H55, D7

Working Paper Number


Copyright/Permission Statement

Opinions and conclusions are solely those of the author(s) and do not reflect views of the institutions supporting the research, with whom the authors are affiliated, or the Pension Research Council. Copyright 2010 © Pension Research Council of the Wharton School of the University of Pennsylvania. All rights reserved.


This research was supported by the U.S. Social Security Administration through grant #10-P-98363-1-05 to the National Bureau of Economic Research as part of the SSA retirement Research Consortium

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Economics Commons



Date Posted: 07 August 2019