Andrew Biggs, an economist at the American Enterprise Institute, had a piece in the Hill telling readers that the private 401(k) system is doing just great, while public pension plans and Social Security are in big trouble. The story is we need not worry about most people’s retirement security, we have to worry about the cost of the public retirement system.

There are a few parts of Biggs’ story that don’t quite hold up. Biggs tells us:

“A 2016 Census Bureau study found that — thanks to a 75 percent increase in benefits from private retirement plans — incomes for the median new retiree rose by 58 percent above inflation from 1989 to 2007. Another new study, from economists at the IRS and the Investment Company Institute, finds that the median retiree has an income equal to 103 percent of their income just prior to retirement, far exceeding the 70 percent “replacement rate” that most financial advisors recommend.”

The Census Bureau study actually was just looking at the retirement income of women, not all new retirees. This matters because the median women retiring in 2007 had far more years in the workforce than the median woman hitting retirement age in 1989. Also, women actually did some increase in their pay over this period, in contrast to the stagnation in pay for men earning near the median. So it matters hugely that this study was only examining women, not all retirees.

It is also important to note that the use of the term “income” is somewhat misleading in this paragraph. It is including as income withdrawals from IRAs and 401(k)s. This is somewhat problematic since this is drawing down past savings, it does not amount to an ongoing flow. The studies cited by Biggs don’t indicate if the pace of drawdown in the years immediately after retirement can be sustained for a retirement that could last 25 years or more. (Biggs is correct to point out that the money taken out of 401(k)s is largely excluded from other data measuring income. While it is wrong to ignore this money, it is not right to treat it as income in the same way that a traditional defined benefit pension is income.)

For example, if someone has $100,000 in a 401(k), they can withdraw $20,000 a year for five years. After that point, they will have exhausted their funds. It is likely that many retirees will find themselves in this situation. According to data from the Federal Reserve Board’s 2013 Survey of Consumer Finance, the middle quintile of households with a respondent between the ages of 55 and 64 had non-housing wealth of just $89,300. This will not allow for any substantial spending in retirement for any long period of time. And the bottom two quintiles of course have near zero in retirement savings.

In addition, those now approaching retirement had far smaller share of their homes paid off than was the case in the 1980s. This means that they could expect to paying off a mortgage long into retirement, unlike retirees from three decades ago.

On the other side, Biggs tells readers:

“According to Federal Reserve data, public employee retirement plans run by the federal, state, and local government have promised Americans $45 trillion in future retirement benefits.

“But government employee plans only have $33 trillion in funding, leaving a $12 trillion gap. On top of these shortfalls, Social Security faces an additional $12 trillion-plus funding shortfall. If Social Security became insolvent, all bets are off: the 25 percent across-the-board benefit cut that would occur around 2030 would pummel middle-income retirees and crush the poor.”

Actually, the vast majority of public pension plans are well-funded. Normal market rates of return will fill most of the $12 trillion funding gap. While there are places like New Jersey and Kentucky, where politicians from both parties have made a sport of not properly funding pensions, most states have funding levels that will be sufficient to pay benefits through their 30-year planning horizon.

Telling us that Social Security faces a shortfall of $12 trillion may sound scary, but it is important to remember that this is total calculated over its 75-year planning horizon. This comes to 0.95 percent of projected GDP over this period. That is not a trivial amount, but by comparison, Donald Trump’s proposed tax cut is roughly three times this size.

It will be necessary to increase funding for the program at some point. Much of the projected shortfall is due to the upward redistribution of wage income over the last four decades. It can be closed to a substantial extent by raising the cap on income subject to the tax, although some increase in the payroll tax, like we had in the decades of the forties, fifties, sixties, seventies, and eighties, may be appropriate at some point.

If workers get their share of the gains from productivity growth it hardly seems a disaster to take back some of these gains to support a longer retirement. Of course if the typical worker continues to see little or none of the benefits from productivity growth any tax increase will be a problem. But the issue here is the policies that are preventing workers from sharing in the gains from growth, not Social Security.