The U.S. government has saved more than $1 trillion in debt since 2007 because of the actions taken by the Federal Reserve to stimulate the economy, a new report from the McKinsey Global Institute finds.

By keeping short-term rates near zero and engaging in large-scale asset purchases known as quantitative easing, the Fed also boosted U.S. banks' net interest income by $150 billion, the analysis found.

The government profited by being able to issue Treasury debt that pays lower interest rates. The effective rate on outstanding U.S. debt fell from 4.8 percent in 2007 to 2.4 percent in 2012, according to the study, saving the Treasury $900 billion in interest payments over that time. The Fed also remitted an extra $145 billion in profits to the Treasury during that period.

Meanwhile, by allowing big banks to borrow at near zero interest rates and lend out at higher rates, the Fed's zero-rate policies have helped bank's bottom lines.

In addition to creating winners, quantitative easing and zero rates have also created losers. American households missed out on $360 billion in net interest income. Younger Americans, who are net debtors, benefited from the policies. But those above age 55, who are savers, lost out. Americans 75 and older, according to the report, "lost an average of $2,700 a year in income."

By inflating home and bond prices, however, the Fed's stimulus efforts lifted household wealth in the United States by up to $5.6 trillion, the study estimates. That run-up in wealth also translated to roughly $167 billion in added consumer spending in 2012, aiding the broader economy. Those effects, the study's authors estimate, "far outweigh the income lost to households."

The study's lead authors, MGI's Susan Lund and Richard Dobbs, note that their research is constrained by the fact that they can't directly assess what would have happened to the U.S. economy in the absence of the Fed's quantitative easing efforts. They also note that, no matter what distributional effects they find, "it seems likely that central bank actions stabilized the financial system, limited the damage from the financial crisis, and dampened the recession, thereby benefiting all actors in the economy."

The McKinsey Global Institute is the research arm of McKinsey & Company, a management consultant.

The Fed's balance sheet has grown from less than $900 billion in assets just before the crisis in 2008 to nearly $4 trillion today. It is currently purchasing $85 billion every month in Treasury and mortgage-backed securities, and is expected to slowly reduce that amount throughout next year. Fed officials have indicated that they anticipate keeping short-term interest rates near zero through 2015.