The state and the federal government are arguing over a million Californians. The state says they exist. The U.S. Census Bureau says they don't.

The Census Bureau released population estimates Thursday that say California remains the nation's most populous state with 36.5 million residents — including nearly 1.5 million in Alameda County, 1.7 million in Santa Clara County, 744,000 in the city and county of San Francisco, and some 705,000 in San Mateo County.

But figures from the state Department of Finance say there are 987,000 more people in 2006 than estimated by the Census Bureau. And some of the largest estimate gaps are in the Bay Area, with the state saying Alameda, San Francisco and Santa Clara counties each have about 60,000 more people than the Census Bureau estimates. That's roughly the population of Palo Alto for each county. In San Mateo County, the difference is about 23,000 people, while it's about 10,555 people in Contra Costa County.

The growing disparity is not just an arcane debate among demographers but has potentially costly consequences to the regions involved. As much as $200 billion in annual federal aid to the states is parceled out based on population estimates. Local planners and corporations use the numbers to decide where to build new fire stations, hospitals and shopping malls.

San Francisco County had the largest percentage gap of any in California by about 8 percent. The state's population estimate for San Francisco as of July 2006 is about 803,000 people, while federal government counts 744,041. Alameda County's count was nearly 4 percent off, with the state counting 57,483 people more than the federal government.

"This difference is just phenomenal," said Hans Johnson, a demographer for the Public Policy Institute of California, a nonprofit think tank that relies on data from both sources. "It really hasn't mattered which numbers you chose in the past, because they really weren't so far apart. But now it does matter."

The growing gap — also an issue for Utah and Colorado — could have political ramifications. In the once-a-decade reapportionment of Congress and state legislatures, people equal power. The present estimate gap in California amounts to the population of about one and a half congressional districts. Estimates are not used for redistricting, but state demographers worry that if estimates don't find people now, the actual Census count in 2010 could miss them as well.

"It's certainly a concern," said Bill Schooling, a demographer for the state Department of Finance. "It's my opinion that if you're expecting to find 10,000 people in a city and you only find 8,000, you're going to look a little bit more, a little bit harder, to see what's missing."

But Chuck Purvis of the Metropolitan Transportation Commission, the transportation planning agency for the nine San Francisco Bay Area counties, dismissed such concerns. He said state demographers use the Census Bureau's decennial count as the baseline for their numbers, and that in 2010, the numbers will be adjusted so they match.

He said that much of the federal transportation money California sees is apportioned based on the decennial census, not on population counts the federal government does in between.

"Eventually, things will reconcile," Purvis said. "It just may be a bit painful that all these intermediate years that you've been monitoring so carefully can be adjusted."

In Utah, the difference between Census and local population estimates is about 65,000 people, but the percentage gap is roughly the same as California's, at about 2.6 percent.

"It's a definitely a concern for Utah, because the divergence between the estimates produced by our local experts and the estimates produced by the Census Bureau are not only different, but the divergence is increasing," said Robert Spendlove, Utah's state demographer.

Because there are so many federal programs based on population estimates, and because population often is only one component in a complex series of variables within the formula for federal grants, the exact dollar impact on federal funding to state, county and local governments is virtually impossible to measure, say state and federal officials and other experts. 

But Census population estimates play a role in a wide array of federal programs that flow to California — from grants to early childhood education and social services, motor carrier safety, public water improvements, surplus commodity food grants, services for senior citizens and much more.

In terms of the amount of federal money based on the population estimates, "it would be very safe to say it's in the tens of millions and likely somewhat in excess of $100 million," said Tim Ransdell, director of the California Institute for Federal Policy Research. "But those are very much seat-of-the-pants guesses, because there have not been good data run."

For both the Census Bureau and the state, yearly population estimates are based on the once-a-decade Census count. The 2000 Census counted 33.9 million people in California. By 2003, the estimates done by the Census Bureau and the state were about 500,000 people apart — about 50,000 in Santa Clara County — and the difference has continued to grow.

"When you're 100,000 people apart, it's not very noticeable when you're dealing with over 30 million people," Schooling said. "But because the difference keeps expanding every year, you've got that cumulative effect."

Population estimates are based on records for births and deaths, and on migration inside the United States and from abroad.

Much of the growing disparity, demographers say, is because the use of different methods for estimating people moving between California and the other 49 states.

To gauge migration, the state uses administrative records including drivers' licenses surrendered by people moving into California.

The Census Bureau relies on Internal Revenue Service records of taxpayers who file from different ZIP codes in consecutive years.

Both acknowledge that neither method is perfect, but Department of Finance demographers say their estimates were more accurate when the 2000 Census was taken.

They say the IRS data misses some people, such as people working in the cash economy or students moving to California to attend college, who don't file an income tax return. Census officials, meanwhile, say they have to use the same methodology for every state to assure equality, and can't always take into account local data like California driver's licenses.

"It's obviously a concern," said Greg Harper, a demographer with the Census Bureau's population division. "We don't really have an objective truth ... it could be the truth is somewhere in between."

California and federal demographers are talking about the problem, and those talks are likely to intensify next week, when a group of demographers from the states meet with census officials in New York.

"We are talking to California about looking at what they've done and whether we need to make any changes in our methods or in their estimates," Harper said. "Right now, we don't have a plan to change our method. That may change in the future."

Contact Mike Swift at mswift@mercurynews.com or (408) 271-3648.