Abstract — This paper proves that the stock-bond portfolio choice of the public social security trust fund is Arrow-Debreu equivalent to the tax treatment of private capital income by the non-social security part of government: the state-contingent consumption of every agent is the same under both policies. A larger [smaller] share of social security’s portfolio invested in stocks is equivalent to a larger [smaller] symmetric linear tax on the risky portion of capital income returns received on assets held by private agents. The tax change causes agents to adjust their private portfolios so that the total (private plus public) levels of demand for equities and bonds are the same under both policies.
At first, it would seem that this equivalency requires that there are no pre-existing tax distortions or market frictions. However, the equivalency is shown to be quite general. First, the initial tax rate on private capital can be non-zero, and the initial tax can take any form (hence, possibly different form than the new tax). Although the amount of revenue collected at the initial tax rate (i.e., not including the rate change) is disrupted after private agents alter their portfolio, this pre-existing tax distortion does not undo equivalency. Second, since private trading with the unborn is impossible, trading markets between generations are allowed to be missing. It follows that the social security trust fund’s stock-bond portfolio choice is not neutral since risk is transferred across non-trading generations. But policy equivalency still holds. Third, an arbitrarily large share of agents (short of everyone) can even be borrowing constrained. Borrowing constrained people do not even have a portfolio of assets that can respond to taxes. Still, while consumption levels vary by state and agent type, they are identical under both policies, even for the constrained.
To the extent that trust fund investment in equities improves risk sharing in the context of missing or incomplete markets, as shown in some previous papers, the equivalent capital income tax rate can be interpreted as a Lindahl (corrective) tax. This tax gives a decentralized way of achieving the same potential risk sharing outcomes as the government directly owning part of the capital stock. The decentralized approach to improving risk sharing might be more palatable to those who fear direct government intervention in financial markets (e.g., Greenspan, 1999). General-equilibrium simulation results are presented using an overlapping-generations model with aggregate uncertainty. The model incorporates a fully endogenous equity return distribution, and several other features that have been taken as exogenous in previous models. The model is used to produce policy-equivalent tax rates along the non-neutral ex-post mean transition path from the initial stochastic steady state (before the trust fund is invested in equities) to the final stochastic steady state (after the trust fund is invested in equities). The results suggest that investing the entire US Social Security trust fund in equities is equivalent to a 4 percent tax on risky capital income tax returns. This equivalent tax rate is fairly constant along the mean transition path.