An independent analysis of California’s three big pension funds has found a hidden shortfall of more than half a trillion dollars, several times the amount reported by the funds and more than six times the value of the state’s outstanding bonds.

Graduate students at Stanford applied fair-value accounting principles to California’s pension funds, using a method recently devised by two economists working in Illinois, Joshua D. Rauh of Northwestern University and Robert Novy-Marx of the University of Chicago.

The Stanford group’s finding does not suggest that California has to come up with half a trillion dollars all at once; pensions are paid slowly over time. But the possibility that the state’s public pension funds are much deeper in the hole than reported could help explain why the required contributions to the funds have been rising every year, contributing to California’s annual budget drama. The rest of The New York Times story is here and the Stanford report can be found here.