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Sunday, March 13, 2005

Personal Accounts and aggregate saving.

I am going to attempt a medium serious analysis of the effects of personal accounts on aggregate private saving. I think it is clear that, other things equal, they would cause a reduction in private saving making it more not less difficult to finance both the retirement of baby boomers and capital formation.

tIt is agreed that the plan will require the government to increase borrowing to pay current benefits. It is claimed that this is no problem, because it is like pre-paying a mortgage. This argument is silly, because pre-paying a mortgage can be a very costly mistake. In particular, if the mortgage interest rate were as low as the return on social security contributions, it would be a very bad idea to pre-pay a mortgage.

Now to discuss personal accounts, one needs to know what exactly the Bush plan is. Bush is keeping it secret so I will make two guesses.

The first is that for every dollar put into personal accounts the guaranteed benefit will be reduced by an amount such that the expected loss in guaranteed benefit discounted at a real interest rate of 3% has a present value of $1. I will call this plan 1.

Under plan two the guarnateed benefit will be multiplied by the fraction of contributions not put into personal accounts. I assume that if this fraction varies over time, then the amounts are made current to the date of retirement using the rate of growth of average wages as an interest rate (that is dollars at t1 are converted to dollars at t2 by dividing by the average wage at t1 and multiplying by the average wage at t2).

Plan two is more generous than plan 1. The effective return on contributions to social security is, on average, 2%. I read in Brad DeLong's
excellent critique of Greg Mankiw's TNR article that it is "the upper middle class and the rich...effectively borrow from their defined-benefit Social Security account at 1.5% or 2% above inflation to invest their money... poorer Americans ... borrow[ing] from their defined-benefit Social Security accounts at 3% plus inflation?" Thanks Brad.

Also note plan 1 does not offer a better deal to the rich. They get a lower return on contributions to social security but would get the the benefits cut as if they were as generous compared to contributions as they are for the poor.

Personally, I guess plan 1 is more likely, since even Republicans have noticed that they have already given the farm to the rich and they don't want to give them the farm house too. Still I will talk about both. Also Brad assumes that plan 2 will be implemented and *still* seems to think that there is an 80% chance that the effect on national savings will be small. I don't get it.

OK finally the analysis

First I will assume a standard neoclassical growth model with Ricardian equivalence. This is a standard benchmark model. Non-economists will assume that I must be joking. I will assume that aggregates like GNP, interest rates and average wages are perfectly forecastable and that everyone forecasts them perfectly. I will assume that the present value of future tax revenues is equal to the present value of government spending plus the current debt (this isn't really an assumption if I just call a default on debt a tax). Importantly I assume that people belong to infinitely lived dynasties and that each generation leaves a positive bequest to the next. That is, I assume that each person has one parent and 1+n children with 1
In this case, social security reform does not affect aggregate saving. In fact, social security does not affect aggregate saving. Now one might assume that back when social security was introduced it had to cause an increase in the consumption of the first generation of beneficiaries who got something for nothing. It did, but it wouldn't have if they were all giving bequests to their 1+n children and were totally rational. They would have understood that their children were paying for their pensions, saved all the money and given it back when they died if not sooner. Social security is a system which redistributes money from one generation to the other. If everyone is giving bequests, the currently oldest generation is choosing exactly how it wants money distributed among generations, so giving them more money has no effect on the distribution. Clearly this model is not realistic or useful when discussing the effects on savings of social security and its reform.

The model which is generally used is the Diamond OLG model with capital. Same as above except the old give nothing to their children. In this case taking from the young and giving to the old makes the old richer. The first generation of social security beneficiaries definitely spends more. That was, I think, a large part of the point. Remember there was a depression going on and safe nominal interest rates were almost exactly zero making monetary policy ineffective (not to mention the FED was clueless).

In this case an elimination of social security would cause reduced private consumption, since retirees would consume less (in some cases they would consume 0 and starve). However, if currently earned benefits are paid, but no future payroll taxes are collected or benefits earned (elimination with promises kept during the transition) then consumption would increase. The burden of the benefits owed by the currently young to the currently old would be shifted to the public debt. This would eventually have to be repaid generations in the future, but the current young wouldn't care about that and would consume more.

The argument works equally well for plan 2 which would amount to a one third elimination of social security. Because the social security administration has obligations to the old, it must, on average be a bad place to invest compared to the private sector. This is obvious, well known and noted by, among many others, Johnathan Chait in the TNR. Plan 2 would effectively be a huge transfer from the unborn to the currently young, since the unborn would have to pay for promises to the currently old by repaying the huge public debt. Under plan 2, personal accounts are like repaying a mortgage when the bank is currently charging you an interest rate far below the market rate.

Another way of putting this is that, since the return offered by the social security administration is (and must be) below market rates, the present value of the reduction of benefits due to personal accounts must be less than the present value of money diverted into personal accounts. Thus even if one counts the social security shortfall as part of the debt, total public indebtedness would increase if plan 2 were implemented.

Now one might wonder if the Diamond model is a bit hard on the heartless parents. Maybe the model with Ricardian equivalence isn't so far from reality. If so, the increase in public debt due to plan 2 personal accounts would not reduce aggregate saving. Also, if so, budget deficits do not reduce national saving (as is welll known). The argument that plan 2 would not add to the deficit is identical to the argument that deficits don't matter. No one who is concerned by the budget deficit should accept the argument that plan 2 would not reduce aggregate savings.

So what about plan 1 ? I will, for the moment, stick to the assumption that people are rational.
This implies that stock is not underpriced. Plan 1 is much less generous than plan 2, so many people will not set up personal accounts. However, those who do will get a better deal as a result (they are rational). This means that they will be able to afford higher consumption both now and in the future. If they put only treasury bills in their accounts there would be no increase in supply of treasury bills to other buyers. Nor would there be any decline in stock available to other buyers. This means that interest rates and stock prices wouldn't change if there were no other changes in demand. In particular it means that consumption would increase if interest rates did not go up or stock prices go down. The negative effect on aggregate saving would be partially eliminated by an increase in interest rates (as would any negative shock on aggregate saving).

If people put bought other assets with their personal accounts there would be a shift in returns on various assets. the price of t-bills would go down, the price of other assets would go up. This would have no clear effect on aggregate consumption. The consumption of people who sold stock to be put in the personal accounts would not go down as a result. They are rational, they would not sell stock if doing so made them poorer. They will not sell stock if doing so makes them consume less.

If people are rational plan 1 would cause reduced aggregate saving. The effect would be smaller than under plan 2 but it would still be huge if a significant fraction of the population obtained significant advantages from the personal accounts..

Now what if people aren't rational ? If people aren't rational some might set up personal accounts even if social security offers them a better deal. Also people might get excellent returns by buying underpriced stocks from irrational people. The short run effect of private accounts on consumption would be the same. If people irrational think they are richer because they have set up a private account, they should consume more. If people irrationally think they are no poorer after selling underpriced stock, they should not consume less.

Evenutally when people learn they have made a mistake, they will consume less.

This is actually similar to the effect of deficit spending. First higher consumption when the public debt is run up then lower consumption when it is reduced. People who think deficits are a bad idea should think that Plan 1 will have bad effects on aggregate saving, even if they are confident that people who set up personal accounts will eventually rue the day they did.

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