New York (CNN Business) Martin Feldstein, one of the most influential economists of his generation and adviser to presidents of both political parties, died Tuesday at the age of 79.

Feldstein was a professor of economics at Harvard University for five decades, an expert on taxes and a leading advocate of supply-side economics. He was a mentor to conservative thinkers and respected by Democrats. Many of his students went on to play important roles in the field.

Between 1982 and 1984, Feldstein served as chairman of the Council of Economic Advisers and chief economic adviser for President Ronald Reagan. Later he was an adviser to Republican President George W. Bushand then Democratic President Barack Obama

For many years, Feldstein headed the respected National Bureau of Economic Research , or NBER. The group wields enormous influence inside the world of economics and business, but it is little known to the wider public. It conducts influential research on economics and the workings of the markets. It is also the body charged with formally determining when the American economy is in a recession.

In January 2008, a time when the economy was showing early signs of distress that would eventually lead to the near-collapse of global credit markets, Feldstein told CNN Business that he believed a recession was likely. He cautioned that policymakers had better be ready to juice the US economy with tax cuts — known as fiscal stimulus — because Federal Reserve cuts wouldn't be enough.

"What's clear is even if the economy doesn't go into a full scale recession it will be a slow year, one that would benefit from a fiscal stimulus like a $300 (tax credit). If we're going to actually slip into negative GDP, I would want to see more than that," Feldstein said.

In fact, NBER would later determine that the Great Recession had begun in December 2007. It would last through June 2009 and claim millions of jobs.

While Feldstein did not serve in the George W. Bush administration, he was an adviser to the campaign and was seen as a leading force in shaping the administration's tax cut strategy, as well as its failed push to privatize Social Security.

A Harvard colleague, Jeremy Stein, a former member of the Federal Reserve board of governors, called Feldstein "the pre-eminent bridge-builder in the economics profession, someone who did more to bring people and ideas together in a congenial way than just about anyone else."

Jason Furman, a top economic adviser to President Obama, remembered Feldstein as a giant in his field. "He set an example for all of us with his constant and insatiable engagement with economics and policymaking."

Will miss Marty Feldstein. My first teacher in economics and a generous and wise friend and mentor ever since. He set an example for all of us with his constant and insatiable engagement with economics and policymaking.https://t.co/17DWtGrAPp — Jason Furman (@jasonfurman) June 11, 2019

Another leading economist, William Gale of the Brookings Institution, said Feldstein "changed the face of public finance."

I an so sorry to hear about Marty Feldstein. I have tremendous respect for him. He changed the face of public finance. So much of what I think about and work on has been influenced by him. https://t.co/19QfcD0atA — William Gale (@WilliamGale2) June 11, 2019

-- CNN Business' Chris Isidore contributed to this report.