DETROIT — Despite a loss of about $11 billion on the General Motors Co. bailout and $2 billion on the Chrysler Group bailout, the government — and the economy — are better off, according to a new study.

With the Treasury Department’s Monday announcement that the government has sold its remaining shares of GM stock, the Ann Arbor, Mich.-based Center for Automotive Research on Monday released an updated version of a previous study arguing that the collapse of GM and Chrysler would have cost a lot more than the bailouts.

The Center for Automotive Research estimated that the U.S. would have had 2.6 million fewer jobs in 2009 and 1.5 million fewer jobs in 2010 if the two auto companies had disappeared. The study also estimated the government “saved or avoided the loss of” $105 billion in lost taxes and other payments.

Sean McAlinden, senior economist for the center, estimated that the liquidation of GM and Chrysler would have triggered a massive crisis in the automotive industry supply chain. He said many suppliers would have failed, causing widespread layoffs at automakers that didn’t seek government aid.

In addition to GM and Chrysler jobs, the report estimates that 90 percent of U.S. employees at Ford, Toyota, Honda, Nissan, Mercedes and BMW would have been laid off for at least a year.

“When people are not working, not only does the government not collect money, it must spend money,” McAlinden said, pointing to unemployment insurance and food stamps as examples. “Short-run losses are real losses. They don’t go away in the long term, even if the industry does come back.”

Neither GM nor Chrysler contributed to the study.

McAlinden said that manufacturing jobs eventually would have returned, but they would have shifted to the South, while R&D jobs migrated overseas.

General Motors North America President Mark Reuss said the bailout was necessary.

“If you look at … what this did and what it prevented, those are the facts,” Reuss told reporters at an unrelated event Monday morning. “I feel good about that. There’s been tens of thousands of people who can now put food on the table.”

The government’s exit comes about five years after former President George W. Bush launched a bailout that was continued by President Barack Obama’s orchestrated bankruptcy of GM and Chrysler. GM got a total infusion of about $49.5 billion, and the government took an ownership stake in exchange.

The U.S. has recovered nearly $40 billion so far through various measures, including GM’s November 2010 initial public offering, a stock buyback and gradual share sales on the open market.

— The New York Times News Service contributed to this report.