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The Obama administration appears to be using fuzzy math to count the number of jobs created by the $787 billion stimulus package, according to two analyses that show counters included pay raises and hours worked as actual jobs.

The government's claim that the controversial spending bill led to 640,000 jobs could be overstated by at least 20,000 because recipients of federal grants and contracts appear to have made mistakes when estimating the number of jobs that have been saved or created, according to a Wall Street Journal analysis.

And an Associated Press review found that more than two-thirds of 14,506 jobs credited to the stimulus under a popular federal preschool program were overstated because pay increases for existing workers were counted as jobs saved.

The reviews raise fresh questions about the process the Obama administration is using to tout the success of its economic recovery plan -- one in which half the money has been spent so far.

Last week's stimulus report claimed 640,000 jobs saved or created by the economic recovery plan so far. Those jobs came from 156,614 federal contracts, grants and loans awarded to more than 62,000 recipients, worth a total of $215 billion.

Obama has promised the stimulus would save or create 3.5 million jobs by the end of next year, and the data released Friday represented the first head count toward that goal.

The Journal review found that some colleges and universities counted every part-time student's work-study position as a full-time job. And some low-income housing landlords whose longtime contracts with the federal government were funded by the stimulus this year reported a total of 6,463 employees as jobs saved.

Dozens of recipients claimed to have created or saved at least one job with less than $2,000 in stimulus money, for a total of at least 3,300 jobs, according to the Journal review.

The Associated Press found that more than 250 other community agencies in the U.S. similarly reported saving jobs when using the money to give pay raises, pay for training and continuing education, extend employee work hours or buy equipment, according to their spending reports.

Most of the inflated figures were like those cited in the 935 saved jobs reported by the Southwest Georgia Community Action in Moultrie, Ga. The agency, like hundreds of others collecting Head Start money, claimed all its existing employees' jobs were saved because they received a pay raise with the stimulus cash.

The Georgia program inflated the numbers even further by claiming the recovery money saved more jobs than the number of people it actually employs. The agency employs 508 people but claimed 935 jobs were saved because of confusion over government reports.

At Southwest Georgia Community Action Council, director Myrtis Mulkey-Ndawula said she followed the guidelines the Obama administration provided. She said she multiplied the 508 employees by 1.84 -- the percentage pay raise they received -- and came up with 935 jobs saved.

"I would say it's confusing at best," she said. "But we followed the instructions we were given."

Similar claims led to overstating by more than 9,300 the number of jobs saved with more than $323 million in stimulus money distributed by the Health and Human Services' Administration for Children and Families, the AP's review found.

The Bergen County Community Action Program in Hackensack, N.J., noted the nearly $213,000 it received went to cover raises for existing staff only. But it also reported saving 85 jobs.

Republicans have challenged the job-saving claim, saying there was no concrete way to tally jobs "saved."

Ed DeSeve, a senior adviser to Obama on implementing the stimulus, told the Journal Tuesday in a statement that the administration knew the reports were not "100 percent accurate" but that the plan was supposed "to create jobs, not count them."

He added that even the "approximate" total pointed to "tremendous progress."

"We are looking at both overcount reports and undercount reports, and continue to ask questions of recipients to try to fix errors," DeSeve told the newspaper. "In the end, we think any adjustments to the direct jobs count will be modest as a percentage of the 640,000 jobs total, either raising it or lowering it slightly."

Antonia Ferrier, a spokeswoman for Republican House Minority Leader John Boehner, said counting raises as part of the inflated job count "is more than ridiculous."

The AP's new review focused only on the money distributed by the Administration for Children and Families and was not an assessment of the money handled by dozens of other federal programs and other job claims made in the new stimulus report.

The AP's types of accounting errors were found in an earlier review of stimulus jobs that the Obama administration said was misleading because most of the government's job-counting mistakes were being fixed in the new data.

The administration acknowledged overcounting in the new numbers for the HHS program. Elizabeth Oxhorn, a spokeswoman for the White House recovery office, said the Obama administration was reviewing the Head Start data "to determine how and if it will be counted."

But officials defended the practice of counting raises as saved jobs.

"If I give you a raise, it is going to save a portion of your job," HHS spokesman Luis Rosero said.

The raises themselves were appropriate since the stimulus law set aside money for Head Start salary increases, but converting that number into jobs saved proved difficult. The Obama administration told Head Start officials to consider a fraction of each employee as a job saved.

Many Head Start programs around the country went further, counting everyone who received a raise as a saved job.

"It's a glitch in the system," said Ben Allen, the research director at the National Head Start Association. "There was some misunderstanding among some in the Head Start community about completing the reporting requirements."

Allen said a cost-of-living adjustment "may not be viewed traditionally as a job saved, but one could interpret it that, by providing COLA, you're retaining staff."

DeSeve said the Head Start numbers "represent a few percent of all jobs reported" and said the problems would probably be balanced out by other errors that underreported jobs.

"We don't expect any corrections to this data to meaningfully impact the total 640,000 direct jobs," DeSeve said.

Click here to read the Wall Street Journal article.

The Associated Press contributed to this report.