The government’s recent $8,000 cash incentive for first-time home buyers has proved even more costly for recipients than for taxpayers, according to data released Monday. Typical buyers have lost twice as much to price declines as they received from the program.

The median home value fell to about $170,000 in March from $185,000 a year earlier, according to Zillow.com. That means a buyer who closed on a house just before the tax-credit program expired in April 2010 collected $8,000 but has since lost $15,000 in value. Those who bought earlier in the program have done worse; the median price is down $20,000 from March 2009.

The $8,000 first-time home buyers tax credit . . . has brought many new families into the housing market,” the White House boasted in November 2009 upon announcing an extension and expansion of the program. Judging by sales declines since, that seems beyond doubt. Over the past year, the pace of existing home sales has fallen more than 6% and that of new home sales has fallen 22%.

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