State and local governments, struggling to emerge from the aftermath of the financial crisis, face another looming funding gap: in their public pensions. These plans hold almost $3 trillion in assets and cover more than 10 percent of U.S. workers, so they’re an important force in the economy.

Even under existing accounting rules, which make the pension math look good by allowing states to apply an artificially high discount rate to future liabilities, the average state pension plan holds assets equal to only about three-quarters of projected liabilities. The difference amounts to about a half-trillion dollars.

Under a lower discount rate that has been approved by the Government Accounting Standards Board and will have to be used by mid-2014 by states that are not meeting their annual required contributions, the difference is greater.

Using an even lower discount rate, one that many economists prefer, the gap would be as much as $2 trillion. Any way you do the calculation, clearly there’s a big problem.

Yet discussions about how to address it are based on flawed assumptions. The dominant view is that large state and local pension gaps are universal across the country, that they are caused largely by assuming too high a discount rate in assessing future liabilities, and that intransigent unions are to blame for the biggest gaps.

Alicia Munnell, the director of the Center for Retirement Research at Boston College, takes on each of these myths in her new book, State and Local Pensions: What Now? Munnell, with whom I served in President Bill Clinton’s administration, has devoted most of her career to pension issues.

First, she computes a funding ratio — that is, the ratio of assets to liabilities — for each state plan. She finds substantial variation: Five percent of public pension plans, for example, were fully funded in 2010, and 35 percent had a funding ratio of at least 80 percent. On the other hand, 12 percent of plans had severe problems: Their assets were less than 60 percent of their projected liabilities.

The New York state teachers’ fund had assets fully equal to liabilities, whereas the New York City teachers’ fund had assets equal to 63 percent of its projected costs. Illinois, Kentucky and Pennsylvania face enormous gaps, while Delaware, Florida, North Carolina and Tennessee have managed their pension plans relatively well.

Why were some plans so badly underfunded and others not? Munnell’s answer is the biggest surprise in her analysis. She argues that neither the artificially high discount rate nor unions can explain the variation. As she concludes, “The poorly funded plans did not come close to surmounting the lower hurdle associated with a high discount rate; raising the hurdle is unlikely to have improved their behavior. And union strength simply did not show up as a statistically significant factor in any of the empirical analysis.”

The worst-funded plans were not especially generous in their benefits, Munnell found, which is consistent with her argument that union strength isn’t what matters. These plans, though, did tend to share two characteristics: They were disproportionately teachers’ plans, and they used a funding method (called the projected unit credit cost method) that is less stringent than those used by other plans.