Oct. 7 (Bloomberg) -- For $2 trillion, Federal Reserve Chairman Ben S. Bernanke may buy little improvement in growth, employment or inflation over the next two years.

Firms with large-scale models of the U.S. economy such as IHS Global Insight, Moody's Analytics Inc. and Macroeconomic Advisers LLC project only a moderate impact from additional Fed asset purchases. The firms estimate that the unemployment rate will remain around 9 percent or higher next year whether the Fed buys $500 billion or $2 trillion of U.S. Treasuries in a second round of unconventional stimulus.

"This is not a game changer for the economic outlook," said Nigel Gault, chief U.S. economist at IHS Global Insight in Lexington, Massachusetts, whose models show that $500 billion of purchases would boost growth 0.1 percentage point in 2011 and leave the unemployment rate at 9 percent or above for the next two years. "There is clearly a risk that people start to perceive monetary policy as impotent."

The meager impact shows the conundrum U.S. central bankers face. Interest rates near zero have failed to produce the intended cycle of borrowing and spending among consumers and businesses. Unemployment hovering near a 26-year high, partly a symptom of weak demand, keeps downward pressure on prices, and further declines in inflation would raise borrowing costs in real terms, making credit more expensive.

"The danger of not doing anything would be pretty high," said Antulio Bomfim, managing director at Macroeconomic Advisers in Washington. "Expanding the balance sheet might actually help reduce the risk of deflation."

Yields on U.S. 10-year notes have fallen to 2.39 percent from 2.7 percent on Sept. 20, the day before the Federal Open Market Committee said it was prepared to ease policy further to support the recovery. The two-year note yield fell 2 basis points to 0.359 percent at 10:58 a.m. in New York trading and touched 0.3513 percent, the lowest ever.

Fed watchers expect the Fed will take further action at its next meeting Nov. 2-3. Economists predict unemployment will rise to 9.7 percent when the Labor Department releases its September report tomorrow, from 9.6 percent in August.

U.S. central bankers have kept their benchmark lending rate near zero for almost two years. In March, they finished $1.7 trillion in purchases of Treasuries, mortgage-backed securities, and housing agency bonds. A slowdown in growth in the middle two quarters of this year prompted the FOMC last month to warn that inflation rates were "somewhat below" its mandate to achieve stable prices and full employment.

New York Fed President William Dudley, who is also vice chairman of the FOMC, was more blunt in an Oct. 1 speech in New York, calling current levels of unemployment and inflation "unacceptable."

Bomfim and Laurence Meyer, co-founder of St. Louis-based Macroeconomic Advisers, predict the Fed will begin with purchases of close to $100 billion a month starting in November, boosting the balance sheet by as much as $1.5 trillion if necessary.

Purchases of up to $2 trillion would raise the annual growth rate of gross domestic product by 0.3 percentage point in 2011 and by 0.4 percentage point in 2012, Macroeconomic Advisers estimates. Yields on U.S. 10-year notes could fall by as much as half a percentage point.

The unemployment rate would finish at 9.2 percent next year and at 7.7 percent in 2012, the firm estimates. Inflation would only be slightly higher than their current forecast for the personal consumption expenditures price index, minus food and energy, remaining below 1% in both 2011 and 2012. The price gauge rose 1.4 percent rate for the 12 months ending August.