Role of Social Security in Capital Accumulation

I now briefly discuss how Social Security can be introduced as a way of dealing with overaccumulation in the overlapping-generations model. Let us first consider a fully-funded system, in which the young make contributions to the Social Security system and their con­tributions are paid back to them in their old age.

9.5.1. Fully Funded Social Security. In a fully funded Social Security system, the government at date t raises some amount d (t) from the young, for example, by compulsory contributions to their Social Security accounts. These funds are invested in the only pro­ductive asset of the economy, the capital stock, and the workers receive the returns, given by R (t + 1) d (t), when they are old. This implies that the individual maximization problem under a fully funded social security system becomes

subject to

and

9.5.2. Unfunded Social Security. The situation is different with unfunded Social Security. Now the government collects d (t) from the young at time t and distributes this to the current old with per capita transfer b (t) = (1 + n) d (t) (which takes into account that there are more young than old because of population growth).

What this implies is that the rate of return on Social Security payments is n rather than r (t + 1) = R (t + 1) — 1, because unfunded Social Security is a pure transfer system. Only

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s (t)—rather than s (t) plus d (t) as in the funded scheme—goes into capital accumulation. This is the basis of the claim that unfunded Social Security systems discourage aggregate savings. Of course, it is possible that s (t) will change in order to compensate this effect, but such an offsetting change does not typically take place. Consequently, unfunded Social Security reduces capital accumulation. Discouraging capital accumulation can have negative consequences for growth and welfare. In fact, the empirical evidence in Chapters 1-4 suggests that there are many societies in which the level of capital accumulation is suboptimally low. In contrast, in the current model reducing aggregate savings and capital accumulation may be a good thing when the economy exhibits dynamic inefficiency (and overaccumaltion). This leads to the following proposition.

PROPOSITION 9.8. Consider the above-described overlapping generations economy and suppose that the decentralized competitive equilibrium is dynamically inefficient. Then, there exists a feasible sequence of unfunded Social Security paymentswhich will lead

to a competitive equilibrium starting from any date t that Pareto dominates the competitive equilibrium without Social Security.

Proof. See Exercise 9.13. ?

Unfunded Social Security reduces the overaccumulation and improves the allocation of resources. The similarity between the way in which unfunded Social Security achieves a Pareto improvement in this proposition and the way in which the Pareto optimal allocation was decentralized in the example economy of Section 9.1 is apparent. In essence, unfunded Social Security is transferring resources from future generations to initial old generation, and when designed appropriately, it can do so without hurting future generations. Once again, this depends on dynamic inefficiency; when there is no dynamic inefficiency, any transfer of resources (and any unfunded Social Security program) would make some future generation worse-off. You are asked to prove this result in Exercise 9.14.

9.6.