Friday, November 12, 2004
Generational transfers
Brad DeLong has a very nice post on Social Security. His starting point is a thought that confused me (or perhaps beguiled is the better word) as an undergrad econ major. To wit (and I will give the game away by stating assumptions clearly), assume a closed economy, with static production technology, and with overlapping generations of agents who retire in their last period of life. Goods produced in each period must be consumed in that period (they are perishable). Suppose there are N people at any given time, consisting of p*N, 0 < p < 1 workers and (1-p)*N retirees. Also assume that each worker produces g goods per period. Under these assumptions, total consumption in each period will be p*g, average consumption will be p*g/N, and so if the fraction of workers p declines, there will be less to go around regardless of who gets what. We haven't specified an allocation mechanism, but we don't really need to under these assumptions. Unless goods themselves (and not written promises of them) can be produced in an earlier generation and saved for a later one, it doesn't matter how you split the pie among a growing number of retirees---it will be smaller per person.
Social Security is a method for reallocating present production among workers and retirees. It does not involve the saving of goods, or very much saving of promissory notes for that matter. So Kevin Drum wonders what the big deal about how it is structured (private vs government accounts): won't the pie shrink the same either way?
Hopefully, you are quicker than I was when presented with this as an undergrad. If we relax the assumption that the economy is closed, then consumption in a given period could rise above p*g, through international investment or borrowing. But the big point is one BDL raises: if the production technology is endogenous, then more investment early on with increase g over time, so that domestic production can keep up even though p is shrinking. So there is at least a possible argument for private investment of social security funds leading to long run efficiencies. Notice, however, that the investment need not be done by individual accounts; it could be done by the government as a whole. Notice also that what we really need is net private investment to rise. Borrowing money to put in private accounts does jack squat.
Social Security is a method for reallocating present production among workers and retirees. It does not involve the saving of goods, or very much saving of promissory notes for that matter. So Kevin Drum wonders what the big deal about how it is structured (private vs government accounts): won't the pie shrink the same either way?
Hopefully, you are quicker than I was when presented with this as an undergrad. If we relax the assumption that the economy is closed, then consumption in a given period could rise above p*g, through international investment or borrowing. But the big point is one BDL raises: if the production technology is endogenous, then more investment early on with increase g over time, so that domestic production can keep up even though p is shrinking. So there is at least a possible argument for private investment of social security funds leading to long run efficiencies. Notice, however, that the investment need not be done by individual accounts; it could be done by the government as a whole. Notice also that what we really need is net private investment to rise. Borrowing money to put in private accounts does jack squat.
