Trading with the Unborn: A New Perspective on Capital Income Taxation

Security markets between generations are incomplete in the 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 by 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. It shows how the government can replicate these trades by taxing the realized equity premium on investments by either a positive amount or a negative amount. When technology shocks are mostly driven by changes in depreciation, a positive tax on the equity premium replicates the hypothetical trades; this tax is also 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, the equity premium is to be taxed at a negative rate; this tax is also pareto improving. Finally, 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 on the equity premium is pareto improving.