The controversial changes to Illinois’ public pension systems enacted in December came after years of fierce debate. And one of the key points of contention among academics and fund leaders was this fundamental question: Exactly how bad is the pension shortfall?

The number kicked around by politicians and reporters is usually around $100 billion, based on estimates from the state’s five retirement systems.

That is what is known as the state’s “unfunded liability”—a fancy way of saying the amount Illinois will owe state workers in future retirement benefits but will not be able to pay if the systems’ finances do not change.

But there are economists, including a recent Nobel Prize winner, who thinks the real amount of this pension debt is at least two or three times bigger than that.

Economists, lawmakers, and pension fund leaders agree that Illinois’ pension underfunding is a gargantuan problem, no matter what math you use. But the math does matter, they say, because it produces the number they are trying to hit when they determine state contributions or pension reform laws.

The bigger the number, the more taxpayers and state workers may feel the sting in the form of benefit reductions, tax hikes, or budget cuts.

A question of risk & optimism

Jeffrey Brown, a financial economist at the University of Illinois, believes the state’s unfunded pension liabilities are more likely around $250 billion.

He is part of that school of economists who have raised big questions about the way all American public pension funds are crunching their numbers. The result, academics such as Brown claim, is that public pension debt is made to look far smaller than it really is.

“They’re being too optimistic because they are failing to account for risk,” Brown said.

At issue are the assumptions that pension funds make about how much money they will earn off of their investments in the future.

Running a public pension fund is basically like being a fortune teller, with a calculator instead of a crystal ball. Pension fund actuaries try to predict how much of today’s dollars they will need in order to pay retirement benefits decades down the road.

To do that, they also try to predict how much money they are going to make from their investments. The more they assume their investments will grow in the future, the smaller they assume their future pension debt will be.

The number pension funds use to predict their future financial condition is called a “discount rate.” Right now, Illinois’ five state pension funds assume those investments will bring in 7 percent to 8 percent a year. Many pension funds in Illinois have hit or exceeded that mark when returns are averaged over the last 30 years.

But economists such as Brown argue that assumption is too optimistic, regardless of what happened in the past.

“If I go to Las Vegas, and I bet my house, and I actually win, it doesn’t mean that it was a smart thing to go to Las Vegas and gamble my house, because I could have just as easily lost,” Brown said.

Brown said a safer rate of return would be around 4 percent, and some economists have said it should be even lower. But there is a more fundamental issue, he said. Because public pensions, unlike 401(k) plans, are supposed to be guaranteed payments to workers, pension funds should not be using something as unpredictable as investment returns to discount what they will owe.

“Whether you invest the money…in Beanie Babies, or whether you invest it in stocks, or whether you put it under your mattress, doesn’t affect how much we owe,” Brown said. “And the same thing is here. They’re really separate decisions.”

The ‘reality’ of public pensions

Brown’s pitch of new pension math has not gone over well with many pension fund leaders.

“What you’ve just described is pure finance theory,” said Keith Brainard, director of research at the National Association of State Retirement Administrators, which represents public pension leaders nationwide. “However, public pension plans are not operating in a world of theory.”

Brainard has been a vocal critic of the more conservative math that economists such as Brown are advocating. He points out that the funds’ financial predictions are not simply based on past investments, but also on what they think will happen in the future with interest rates, inflation, and the performance of a wide range of assets.

And he sees an agenda behind some financial economists’ estimates, which would make America’s public pension problems seem so bad as to be almost unsolvable, absent huge tax hikes or deep budget cuts.

“It would make the cost of providing that benefit so prohibitive that state legislatures and city councils by and large would be forced to close those pension plans,” Brainard said.

Some economists have predicted that very outcome. Brainard dismissed that notion as a scare tactic, often wielded by groups that believe public pensions are unsustainable, and that workers should be shifted over to 401(k)-style retirement plans.

Illinois’ challenging pension math

State Sen. Daniel Biss, D-Evanston, was one of the architects of the state’s new pension law. He said the type of pension math advocated by some financial economists would be particularly hard for Illinois’ cash-strapped state government.

Assuming less money from future investments would mean Illinois must kick in more money to pay for pensions — perhaps too much money, if investment returns exceed the lowered expectations.

And Biss said Illinois simply cannot afford to be conservative with its math, but rather needs to try to guess its pension obligations right on the nose.

“If we had enough money as a state to - in addition to funding schools and health care and human services and infrastructure - also create a Scrooge McDuck-style vault of coins for the pension systems to play in for no reason, I think that might be a cool tourist attraction,” Biss said.

But not a practical one.

Still, for financial economists like Brown, this whole debate is about transparency. Brown does not advocate for the abolition of public sector defined benefit plans, but thinks they are not being honest with themselves—or with taxpayers.

“If you’re gonna have those discussions, regardless of where you come down, you need to be working with accurate numbers, “Brown said. “And you don’t want to hide the true cost of things.”

Alex Keefe is a political reporter at WBEZ. You can follow him on Twitter and Google+.