Alan Greenspan believes the economy would thrive if America let more immigrants into the country.

The former Federal Reserve chair says the highly skilled migrant program -- the H-1B visa that is popular with tech companies -- should be a lot bigger.

"The H-1B visa program is much too small," Greenspan said Thursday at the Council on Foreign Relations in New York. "If we really wanted to increase productivity, we would really open that program up."

This year a record 233,000 foreigners applied for only 85,000 H-1B visas.

He believes anyone who gets a PhD in the sciences in the United States should be allowed to stay.

Greenspan was speaking a day after the Fed raised interest rates for the first time in nearly a decade.

He wouldn't say much about the Fed's move, but he did praise current Fed chair Janet Yellen and the committee for sending clear signals. He said the Fed prepared the markets well for the move and it reassured investors there would not be a series of rapid rate hikes.

"Basically, the markets just said the uncertainty is gone," he said. Stocks rallied Wednesday after the announcement.

Related: Finally! Fed raises interest rates

While America's economy has improved enough for the Fed to raise rates, it is still underperforming. Greenspan blames Congress.

Politicians have not only failed to do immigration reform, they have also created a mess with Social Security and Medicare, he argued. They have created a "very unstable fiscal system."

These so-called entitlements are growing at 8% or more a year, Greenspan said. It's a huge drain on the economy. Money that could be going toward education and investment or the next big thing is instead going to retirees.

"Entitlements are the third rail of American politics. You touch it and you lose," lamented Greenspan.

Both parties have made the problem worse, but entitlements have actually grown more under Republicans than Democrats, he said.

Until Congress makes some real reforms -- such as lifting the age when retirees can start collecting benefits -- Greenspan thinks there's almost no chance America will return to its glory days of economic growth.

Historically, the U.S. economy has grown at over 3% a year. But since the 2008 crisis, the economy has struggled to grow much more than 2% a year.

There's been plenty of criticism about Greenspan's tenure as Fed chair. Some say he helped cause the dot-com bubble and the housing crisis. Greenspan defends his decisions.

"Anybody who thinks being head of the central bank is a delightful activity, let me disabuse you. It's torture," he says.