WASHINGTON -- A controversial proposal that would save the government billions by changing the way Social Security benefits are adjusted each year would actually give seniors more spending money, Republicans in the House of Representatives claimed Monday.

The so-called "chained CPI" is an alternate version of the consumer price index that the government uses to calculate cost-of-living adjustments for Social Security and other programs. The Congressional Budget Office says switching to the chained CPI would reduce Social Security spending by $127 billion over 10 years.

But the House Ways and Means Committee, which oversees Social Security and is led by Rep. Dave Camp (R-Mich.), said the policy would have given seniors a bigger increase than they'll be getting from the regular inflation gauge next year.

"If the more accurate chained CPI was used to determine the 2014 cost of living increase, seniors would see a 1.7 percent increase as opposed to this year’s increase of 1.5 percent," Ways and Means Republicans said on their website. "What does a 1.7 percent increase mean? On average, that is an extra $21.60 each month for seniors to use on groceries, bills and medicine. "

The Alliance for Retired Americans, an advocacy group that opposes Social Security cuts, says the Republicans of the Ways and Means Committee are lying. "The chained Consumer Price Index would be a cut in benefits –- that is why conservatives support it," alliance director Edward F. Coyle said in a statement.

Every October, the Bureau of Labor Statistics calculates cost-of-living adjustments by comparing price indexes from the third quarters of the current and previous year. The indexes used for the chained CPI, however, are revised over a period of two additional years. To calculate their more generous version of the chained CPI, Ways and Means Republicans apparently used the initial chained CPI estimates for the third quarters of 2012 and 2013, even though the bureau had produced an updated version of the 2012 number.

“Any economist will tell you, to use an earlier estimate for a figure -- as they did -- when an adjusted, more accurate number is available, is not sound analysis," Coyle said.

Using the more recent number would have yielded the same 1.5 percent cost-of-living adjustment as the traditional CPI. When the final numbers are available in 2015, the retrospective adjustment the measure would have given seniors this year will likely be lower. Since 2000, the chained CPI would have provided cost-of-living adjustments three-tenths of a percentage point smaller than those provided by the regular measure, according to the Congressional Budget Office.

A spokesman for Camp did not respond to a request for comment.

The Congressional Budget Office's Jeffrey Kling testified during an April hearing that if Congress put chained CPI in place next year, "Social Security benefits would be roughly $30 a month lower, on average, by 2023 than they would be under current law, representing a reduction of about 2 percent of average benefits."

President Barack Obama has repeatedly signaled openness to the chained CPI as part of a "Grand Bargain" budget deal with congressional Republicans, who are even bigger fans of the idea. Opponents argue that the delay in calculating the official value of the chained CPI is one reason not to implement the policy. They also say it would be wrong to reduce benefits for retirees, 47 million of whom receive about $1,204 per month.

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