Sunday, April 20, 2008

How much is a child worth to Social Security?

Recently, analysts on the political right have debated the merits of "family friendly" tax cuts versus tax policy designed for economic growth, in particular, reductions in marginal income tax rates. (See also here.) This is a complex question on which I'm not fully qualified to comment, but here are a few basic points, plus a calculation specific to Social Security (on which, presumably, I am qualified to comment).

First, family friendly tax cuts can increase economic growth down the road if reductions in the cost of having children increase the number of children families have. Since today's child is tomorrow's work, total GDP can be expected to increase along with fertility. Whether GDP per capita increases is another story (that is, it's unclear whether a family having an additional child will improve the economic prospects of other children).

Second, if family friendly tax cuts improve the human capital development of children – say, by enabling a mother to stay home with her children rather than sending the child to day care – then this might also improve economic growth down the road, since human capital is an import contributor to output. Of course, policies such as the child tax credit don't alter incentives to work or stay home at the margin, so the effect is unclear. (In other words, families might use the child tax credit to pay for their daycare…) A more effective incentive actually comes through the Social Security spousal benefit, which is available to non-working spouses but is reduced on a dollar-for-dollar basis by their earned retirement benefits. This effectively increases the net marginal tax on working spouses and so encourages them to leave the labor force. Whether this is fair or good policy overall is a question for another day (I suspect it isn't).

Third – and here's where might be able to add some substance – is the question of how having a child affects the federal budget, in this case Social Security. The Social Security Trustees Report tells us that higher fertility improves Social Security's finances. The sensitivity analysis for the total fertility rate tells that Social Security's 75-year balance improves on a basically a one-for-one basis with increases in the average number of children born per woman. If the total fertility rate rose from the projected value of 2.0 children per woman to 2.1, the 75-year deficit of 1.7 percent of payroll would improve to around 1.6 percent of payroll.

However, this method of accounting is flawed for this question because it measures system financing on a truncated 75-year basis. Cutting off measurement at 75-years increases the measured effect of fertility because it counts all the taxes paid by these new children but not all the benefits that would be owed to them, since much would occur after the 75th year. A solution is to calculate the effect of rising fertility in the infinite horizon. The Trustees don't make such calculations. (I could run the numbers, though I suspect the effects would actually be negative, much as the effects of economic growth are negative in the infinite horizon. This result is counterintuitive and probably not appropriate in this context.)

Instead, I'm here calculating the value of a child on an individual basis. According to SSA's actuaries, the "money's worth ratio" – that is, the ratio of the present value of lifetime benefits received to lifetime taxes paid – is around 0.81 for a single medium wage male entering the workforce today and 0.90 for a single female. Put another way, under scheduled benefits, a single male earner can expect to receive back 81% of his taxes in the form of benefits, while a single female could expect to receive around 90% of her taxes back. Social Security effectively keeps the rest, which implies that more people paying into the program are good for the system's finances.

How good? Using projections of the average wage from the Trustees Report and simulated earnings patterns from the SSA actuaries, I constructed a lifetime earnings path for a medium wage earner. Over the course of his lifetime, a medium wage earner entering the workforce can expect to have earnings worth about $1,159,000 in present value. (The present value of lifetime earnings is the amount today that, earning interest, could produce annual payments equal to the individual's annual earnings.) Assuming the worker bears the full 12.4% payroll tax, his lifetime taxes would equal $149,869. Since the actuaries project that a male would receive around 81% of his taxes back as benefits, his lifetime expected benefits have a present value of $121,394; for a women, where the money's worth ratio equals 0.90, lifetime benefits would total $134,883.

What this shows is that, even if Social Security paid these new workers full promised benefits, they would pay more in taxes they receive back in benefits. For a male, Social Security would pocket $28,475 in present value; for a female, $14,987.

So, purely from Social Security's point of view (emphasis added to avoid confusion), if the program could identify families that are not planning on having additional children, it would make financial sense for Social Security to offer them a cash payment of up to $28,475 to have a boy and $14,987 to have a girl. Anything more than that would be an expected money-loser for Social Security, but anything less than that a money gainer.

Now, this isn't a particularly practical policy, since we can't identify families who would have additional children only for the cash payment, nor can we tell the future earnings of children, which is a big determinant of how much of a financial gain they would be to the program. Nevertheless, this gives a rough idea of the effects of larger families on Social Security's financing.

I've uploaded an Excel file with the calculations for anyone who is interested.


Arne said...

Three comments on the spreadsheet:
1> You have labled the present value taxes to indicate a 2.9% interest rate, but the calculation in for 2.69%. A minor labeling issue, except that your CPI appears to be 2.80% (after the first year).
2> Just to clarify on the wage scaling factor - the drop at the end comes from early retirement and a change in the distribution of workers rather than an expection of income loss for a worker who is still working?
3> The 81/90 numbers are really only good for 2008 and may be significantly different by 2029 when a child added through incentives today actually reaches the 21 years old you used for the spreadsheet.

Arne said...

Assuming I was correct with point three above, it would be interesting to see a history/projection of the 81/90 "money's worth ratio".

Certainly there were some folks who retired in the 50s and 60s who received more than 100%. In fact, since the administrative costs are much less than 10-19%, the amount that Social Security 'pockets' is still going to cohorts that are getting more than 100%.

As we move through the Baby Boomers, do we go through a minimum and start back towards 100%? If we truly prefund Social Security, does that not implay an average benefit ratio above 100% (because the interest earned is more than inflation)?

Andrew G. Biggs said...


Good catches -- my fingers might have been moving too fast for my brain. The real interest rate should be 2.9% and the CPI 2.8%, for an ultimate nominal discount rate of 5.7%. It should be a little different in the near term, but I assumed a constant 2.9% real rate so that's a slight inaccuracy I haven't bothered to fix.

Regarding the drop in earnings as the worker ages, I believe this is due to declining hours of work. The 'scaled earners' are designed to have the same average earnings as a person who works every year and earns the average wage, so I don't believe they really account for years out of the workforce, etc. They're certainly better than simply using steady earners at the average wage, etc., but they do overstate total lifetime earnings somewhat. (For instance, the scaled medium earner is at the 57th percentile of lifetime earnings, so he's a bit above average.)

The money's worth ratios I used were for someone entering the workforce today, so the person was actually born 21 years ago. This is also basically a mistake, but made the numbers easier to calculate. The money's worth ratios for someone born today are actually a little better -- 0.86 for a single male and 0.93 for a single female. However, these are under scheduled benefits and rise due to longer lifespans.

This is where the scheduled vs. payable issue becomes tricky. At some point in the future money's worth ratios would go back above 100% due to rising lifespans, but that's not actually payable under the intermediate projections.

Thanks for catching the mistake. I'll repost the Excel file with the numbers fixed.

Anonymous said...


presumably you are qualified to comment. and if this sort of game amuses you and your friends, that's fine with me.

the mischief comes when you pretend it has anything whatsoever to do with the value of Social Security to the people paying the tax and receiving the benefits.

in particular your moneysworth (present value) calculations depend upon a host of assumptions and unknowables and second order effects neither you nor i are smart enough to calculate.