In 1980, the US government owed, in one fashion or another, $909 Billion, which was about 35% of GDP. Federal spending that year was $591 Billion. If you adjust these numbers for inflation, the 1980 spending was $1,700 Billion and the debt was $2,615 Billion. Today the government spends over $3,000 Billion and the national debt is $19,000 Billion. The current estimates say the debt-to-GDP ratio will be close to 90% this year and will break 100% sometime in the next administration.

I use 1980 as a benchmark because Reagan ran on the debt issue, making it a popular topic in politics ever since. In that time, Republicans have controlled the White House for 20 of those 36 years. They have controlled the House for 18 of those years. The point here is both parties have had chances to arrest the growth of spending and debt accumulation, but neither team has bothered. As long as the Fed can monetize the debt, the politicians keep spending.

Another reason to think back to 1980 is that no one thought the current debt levels were possible. The NYTimes first used the word “trillion” in the 1970’s. The rationale behind Reagan’s tax plan was that making high taxes politically impossible meant spending would have to decline. After all, who in their right mind would keep buying bonds, even at the elevated rate of 10% for the 10-Year Treasury?

The future turned out to be a very different place than the planners of the 1980’s imagined. That’s important to keep in mind when you see stories like this regarding the nation’s public pension systems.

The US public pension system has developed a $3.4tn funding hole that will pile pressure on cities and states to cut spending or raise taxes to avoid Detroit-style bankruptcies.

According to academic research shared exclusively with FTfm, the collective funding shortfall of US public pension funds is three times larger than official figures showed, and is getting bigger.

Devin Nunes, a US Republican congressman, said: “It has been clear for years that many cities and states are critically underfunding their pension programmes and hiding the fiscal holes with accounting tricks.”

Mr Nunes, who put forward a bill to the House of Representatives last month to overhaul how public pension plans report their figures, added: “When these pension funds go insolvent, they will create problems so disastrous that the fund officials assume the federal government will have to bail them out.”

Large pension shortfalls have already played a role in driving several US cities, including Detroit in Michigan and San Bernardino in California, to file for bankruptcy. The fear is other cities will soon become insolvent due to the size of their pension deficits.

Joshua Rauh, a senior fellow at the Hoover Institution, a think-tank, and professor of finance at the Stanford Graduate School of Business, who carried out the study, said: “The pension problems are threatening to consume state and local budgets in the absence of some major changes.

“It is quite likely that over a five to 10-year horizon we are going to see more bankruptcies of cities where the unfunded pension liabilities will play a large role.”

The Stanford study found that the states of Illinois, Arizona, Ohio and Nevada, and the cities of Chicago, Dallas, Houston and El Paso have the largest pension holes compared with their own revenues.

In order to deal with the large funding shortfall, many cities and states will have to increase their contributions to their pension funds, either by raising taxes or cutting spending on vital services.

That’s one possible future. The important thing to remember is the US government has no money of its own. It either taxes, borrows from foreign sources or creates credit money through the machinations of the Federal Reserve. Given the state of the federal budget and projected debt, it’s unlikely the Feds could bailout the state pension systems completely. The CBO says the total debt could hit $30,000 Billion in ten years.

The other possible future is the pensioners don’t get paid. When a company goes bankrupt, the creditors don’t get paid. At least they don’t get paid in full. When cities and towns can no longer make their pension payments, they will stop making those payments. The old retired employees will sue and petition their legislatures, but you can’t get blood from a stone. The best case is the pensioners take a hefty cut in benefits.

The thing no one discusses is why these funds are in trouble. The reason for the trouble is the artificially low bond rates we have seen for two decades. In order to finance Federal spending, borrowing rates have been driven down to near zero. The biggest buyers of treasuries used to be pension funds. They could expect a return exceeding their target of 7.5% and not carry much in the way of risk. Being a pension fund manager used to be the easiest job in finance.

Olivia Mitchell, a professor at the Wharton School at the University of Pennsylvania, told FTfm last month that US public pension plans face “grave difficulties”.

“I do believe that US cities and towns will continue to suffer, and there will be additional bankruptcies following the examples of Detroit,” she said.

Currently, states and local governments contribute 7.3 per cent of revenues to public pension plans, but this would need to increase to an average of 17.5 per cent of revenues to stop any further rises in the funding gap, the research said.

Several cities and states, including California, Illinois, New Jersey, Chicago and Austin, would need to put at least 20 per cent of their revenues into their pension plans to prevent a rise in their deficits, while Nevada would have to contribute almost 40 per cent.

Mr Rauh’s study claims the “true extent” of funding problems in US public pension system has been obscured because plans calculate both their costs and liabilities on the assumption they will achieve returns of between 7 and 8 per cent a year. The academic believes this rate is “wildly optimistic and unlikely to be achieved”.

Mr Rauh said a more realistic return rate, based on US Treasury bond yields, was around 2-3 per cent a year.

Ultra-low bond rates have forced pension funds into higher risk investments as they try to hit their target of 7% per year. This is fine when the market is performing at or near its historic averages and the fund managers are smart enough to bet the broader market. It also assumes that cities and states pay their pension obligations, without actually borrowing from those same pension funds. Now we know why the pension system is in trouble.

This is just one small aspect of the daunting math facing the United States over the next decade. Again, no one imagined the current math was even possible 35 years ago. If you told 1980 people that the Federal debt would be $19 Trillion, they would have laughed in your face. Maybe ten years from now $50 Trillion is no big thing. The math is unimaginable, but today’s math was once unimaginable. Alternatively, perhaps what’s coming is unimaginably awful. I don’t know, but the math problem facing America beggars the imagination.