Robert Novy-Marx is an assistant professor of finance at the University of Rochester’s Simon Graduate School of Business. Joshua Rauh is a professor of finance at the Stanford Graduate School of Business and a senior fellow at the Hoover Institution.

How much will the underfunded pension benefits of government employees cost taxpayers? The answer is usually given in trillions of dollars, and the implications of such figures are difficult for most people to comprehend. These calculations also generally reflect only legacy liabilities — what would be owed if pensions were frozen today. Yet with each passing day, the problem grows as states fail to set aside sufficient funds to cover the benefits public employees are earning.

In a recent paper, we bring the problem closer to home. We studied how much additional money would have to be devoted annually to state and local pension systems to achieve full funding in 30 years, a standard period over which governments target fully funded pensions. Or, to put a finer point on it, we researched: How much will your taxes have to increase?

We found that, on average, a tax increase of $1,385 per U.S. household per year would be required, starting immediately and growing with the size of the public sector. An alternative would be public-sector budget cuts of a similar magnitude, or a combination of tax increases and cuts adding up to this amount.

For some states these numbers are much higher. New York taxpayers would need to contribute more than $2,250 per household per year over the next 30 years. In Oregon, the amount is $2,140; in Ohio, it is $2,051; in New Jersey, $2,000. California ($1,994), Minnesota ($1,928) and Illinois ($1,907) are not far behind.

Most states have traditional defined-benefit pension systems, which guarantee a certain payment upon retirement. In the past 10 years a handful of states have added defined-contribution elements, in which workers share in the market risk of their pension investments, as most private-sector workers do through IRAs or 401(k) plans.

Most of these modifications, however, affect only new hires. Under legislation Virginia passed in April, for example, new employees will have about 40 percent of their defined-benefit pensions replaced by small 401(k)-style plans. As a result, Virginia’s annual household burden of $1,066 will fall around 20 percent. Virginia’s load will remain heavier than that of Maryland, which is in better shape than all but 12 states but nonetheless requires an additional $818 per household each year. Even Indiana, the state in the best condition, would need to increase contributions by $329 per household each year to meet its pension obligations.

These finding were calculated assuming that states invest somewhat cautiously and achieve annual returns of 2 percent above the rate of inflation. But even if states continue to make massive bets that the stock market will bail them out, and if the market were to perform as well over the next 30 years as it did over the past half-century (an unprecedented bull market), the required per-U.S. household tax increase would still amount to $756 per year.

And, of course, the returns could be much worse.

Another way of stating the result is that contributions toward public-employee retirement would have to immediately rise to 14.1 percent of every dollar that state and local governments take in for taxes and fees for services (up from 5.7 percent), including such things as state university tuition and motor vehicle fees. If pensions are to be balanced using taxes only, government contributions would have to jump to 22.6 percent of tax revenue, from 9.1 percent in 2009, the most recent available data.

Without these increased contributions, states are digging deeper holes each year. And as happens with all debt, if the debtors wait to pay it down, they will pay even more down the line.

Nor is it likely that we can grow our way out of this problem. Each additional percentage point of growth in gross domestic product reduces the required increase by $120 per household per year, so more economic growth would help — but typically when the economy as a whole grows, public-sector employment and compensation grow as well, which means more pension promises.

How about increasing public-employee contributions? To obtain the necessary amount, contributions would have to rise by 24 percent. Cutting public employees’ take-home pay by this magnitude is infeasible and would place a huge burden on younger public employees.

In short, some redirection of taxpayer resources to cover pension obligations seems inevitable. In addition, states must enact forward-looking reforms that will stop the explosion of pension debt.

Systems could consider introducing mixed defined-benefit and defined-contribution plans for all employees, not just new hires, a method used by Rhode Island. Most public workers in that state are now in hybrid plans with a smaller defined-benefit component, contributions to individual accounts and higher retirement ages. Combined with a temporary suspension of cost-of-living adjustments, Rhode Island’s reforms reduced the unfunded liability by more than 40 percent.

Cost-of-living adjustments should continue to be reexamined across the country, and new designs should also be considered. Group defined-contribution plans, for example, would leave the responsibility for managing pension money in the same professional hands as it is currently but without the current extent of government guarantees.

The bottom line is that, as long as government accounting standards allow systems to justify low contribution levels by using optimistic guesses about returns that can be earned on portfolios of risky assets, traditional public-employee defined-benefit plans will generate more and more debt. And without reform, the eventual cost of funding these plans will, someday, make the $1,385 per-household increase required today seem cheap.