WASHINGTON (AP) — Ben Carson botched the economic effect of minimum wage increases. Jeb Bush again pitched a dubious target for economic growth. Marco Rubio, in a tale about plumbers and philosophers, undersold the value of a college education.

And Ted Cruz showed just how hard it can be to name government agencies when, just like Rick Perry four years ago in a famously misbegotten moment in a GOP debate, he messed up the list of departments he would close as president.

The fourth debate of the 2016 Republican presidential campaign was thick on economic policy — and with that came a variety of flubs and funny numbers.

Some of the claims Tuesday night and how they compare with the facts:

CARSON: "Every time we raise the minimum wage, the number of jobless people increases."

THE FACTS: Actually, that usually doesn't happen. When the minimum wage was increased in 1996 and 1997, the unemployment rate fell afterward. In June 2007, when the first of three annual minimum wage increases was implemented, the unemployment rate was unchanged until the Great Recession began six months later.

Economic research has found that when states raise their minimum wages higher than neighboring states, they don't typically fare any worse than their neighbors.

It's not known, though, what would happen to jobs if the minimum wage were doubled to $15— as many fast-food workers who demonstrated before the debate were demanding.

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RUBIO: "Welders make more money than philosophers."

Not so, on average.

Rubio is arguing that the U.S. has failed to invest in vocational training — a point also stressed by President Barack Obama's now-defunct jobs council. But Rubio is wrong to suggest that studying philosophy is a waste of money and time.

PayScale, a firm that analyzes compensation, put the median mid-career income for philosophy majors at $81,200 in 2008, with welders making $26,002 to $63,698.

And Georgetown University's Center on Education and the Workforce said in a 2014 analysis that median incomes were $68,000 for people with an advanced degree in philosophy or religious studies.

So knowing Plato and getting a college degree still pays off.

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CRUZ, holding out his hand and unfolding one finger at a time to punctuate his point: "Five major agencies that I would eliminate: the IRS (his thumb), the Department of Commerce (index finger), the Department of Energy (middle finger), uh, the Department of Commerce (ring finger), and HUD (pinkie)."

THE FACTS: He flubbed his own list, naming the Commerce Department twice and leaving out one of the agencies he proposes to close, according to his website: the Education Department.

Perry, then Texas governor, had almost precisely the same problem at a GOP primary debate in November 2011, coming up with the names of only two of the three departments he wanted to close, Commerce and Education. "Oops," he said after failing to name the third agency, Energy, a slip that haunted him for the rest of his campaign.

But Cruz moved on without anyone calling him on the gaffe.

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BUSH: "We could get to 4 percent growth."

THE FACTS: That's a highly improbable target because of forces in the economy that are beyond the control of any president.

Those forces have been decades in the making: an exodus from the workforce of the huge generation of baby boomers, rising automation and low-wage competition overseas. Those factors and more have limited income growth, which in turn cuts into the consumer spending that drives most economic growth.

Bush frequently holds out hope of 4 percent growth, but even conservative economists who like his fiscal and tax plans consider it a false hope. According to current forecasts, growth is expected to average roughly half that rate.

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DONALD TRUMP: The Pacific trade agreement signed by President Obama with 11 other nations "was designed for China to come in through the back door and take advantage of everyone. ... China takes advantage (of the U.S.) through currency manipulation."

THE FACTS: The Trans-Pacific Partnership trade pact, signed last month, does not include China and is intended to give the United States more influence in Asia as a counterweight to China's rising economic power. Obama argues that China could join later, but without having any influence on the agreement's terms.

Regarding currency manipulation, Trump is recycling an outdated claim. He has argued that China keeps its currency undervalued by 15 percent to 40 percent, which would make its exports cheaper and more attractive overseas. Yet the Peterson Institute for International Economics, which had criticized China for keeping its currency artificially low, concluded in 2012 that China's currency by then was fully valued. The International Monetary Fund has reached the same conclusion.

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CARLY FIORINA: "Obamacare isn't really helping anybody."

THE FACTS: President Barack Obama's health care law may or may not be good for the country on balance. But it's clearly helping many people.

In the two years it's been in effect, the share of Americans without health insurance has declined to 9 percent, a historic low. People with pre-existing health conditions can no longer be turned away by insurers, and everyone is required to have coverage or face fines.

While the coverage mandate in Obama's law remains highly unpopular, state-run high-risk health insurance pools like the one Fiorina proposes to replace the law have been tried before and failed to solve the problem.

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CRUZ: Since 2008, the economy has grown on average only 1.2 percent a year, showing "the Obama economy is a disaster."

THE FACTS: That average is correct as far as it goes, but it masks the fact that Obama inherited a raging recession in his first year, when the economy shrank by 2.5 percent. In the five years since, the economy expanded an average of 2 percent, more than Cruz's figure but still a relatively weak recovery in historical terms.

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TRUMP: "I will tell you, I don't have to give you a website because I'm self-funding my campaign. I'm putting up my own money."

THE FACTS: This assertion might have been true months ago but no longer is.

Trump's latest campaign finance report, filed Oct. 15 with the Federal Election Commission, shows that of $3.9 million his campaign raised in the latest fundraising quarter just $100,000 came from Trump, and the rest from donors. It was a big change from last spring, when he loaned his campaign nearly all of the $1.9 million it received.

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BUSH: "We need to raise the (banks') capital requirements. ... Dodd-Frank has actually done the opposite, totally the opposite. ... Bigger banks have more and more control over the financial assets of this country."

THE FACTS: Actually, the Dodd-Frank legislation, passed in 2010 in the wake of the worst financial crisis since the Great Depression, has pushed banks to raise more capital — in other words, to obtain more of their funding from investment, rather than debt.

In fact, Dodd-Frank was criticized earlier this year by the right-leaning American Action Forum for effectively forcing banks to raise more capital.

Bush and other Republican candidates suggested that Dodd-Frank sparked bank consolidations, but the mergers actually started in 2008 under George W. Bush. During that year alone, as the market melted down, Wells Fargo took over Wachovia, JP Morgan Chase bought Washington Mutual and Bear Stearns, and Bank of America acquired both Countrywide Mortgage and Merrill Lynch.

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CARSON: Discussing the presence of Russian troops in Syria, added that "the Chinese are there" as well.

THE FACTS: China has no publicly known deployment of military forces in Syria. In recent days, some news reports have suggested that China would send a warship to Syria, but China's foreign ministry has denied that.

China has used its status as a permanent member of the U.N. Security Council to block the U.N. from taking action on Syria, citing a commonly heard argument against violating Syrian sovereignty.