In Tuesday night's Republican debate, Rand Paul argued that a root cause of growing inequality in America is the Federal Reserve and its policy of low interest rates.

"By artificially keeping interest rates below the market rate, average ordinary citizens have a tough time earning interest," Paul said. "As the Federal Reserve destroys the value of the currency, what you're finding is that if you're poor, if you make $20,000 a year and you have three or four kids and you're trying to get by, as your prices rise, these are the people hurt the worst."

This line of argument has some intuitive appeal, as evidenced by the many Republicans in Tuesday's debate who blamed the Fed for America's economic problems. But it actually makes very little sense.

America doesn't have an inflation problem

The most obvious problem with Paul's argument is that Fed policies have actually produced below-average inflation. Data from the Bureau of Labor Statistics show that the average inflation rate since the fall of 2008 has been about 1.4 percent per year. That's below the Fed's longstanding target of 2 percent annual growth. And it's the least inflationary period in the past half-century.

Markets are also projecting that the average inflation rate will be 1.74 percent over the next decade. So there's zero evidence that the Fed is driving up the cost of living for poor people or anyone else.

Low interest rates can be good for ordinary people

Paul ignores the fact that ordinary people don't just save money, they borrow it too. If you've bought a house in the past few years, you probably benefited from today's exceptionally low interest rates. If you bought a house 10 or 20 years ago, you probably benefited from being able to refinance your mortgage at a lower interest rate. That's thousands of dollars in lost income for big banks.

People used to understand that low interest rates are good for ordinary people. Back in the 1990s, politicians would frequently argue that we needed to cut the deficit in order to bring interest rates down. Low interest rates make it easier for people to buy houses and cars, borrow money to start a business, pay for their student loans, and so forth.

People used to understand that low interest rates are good for ordinary people

At the same time, anyone who's saving for retirement by putting cash in a savings account is making a big mistake — whether interest rates are currently high or low. Experts advise people to put their retirement savings into a diversified portfolio of stocks and bonds. History suggests that this kind of portfolio is likely to outperform a conventional savings account over the long run — and it's not as tied to short-term interest rate moves by the Fed.

The Fed has less control over interest rates than you think

The broader problem with Paul's arguments is that the Fed doesn't actually have that much control over interest rates.

Think of a guy driving along a winding mountain road. In one sense, he has total control over where the car goes. If he turns the steering wheel to the right, the car goes right. But that doesn't mean he can drive the car wherever he wants. If he steers too far to the right, he'll go through the guardrail and off the cliff. If he steers too far to the left, he'll run into the mountain on the other side of the road.

The Fed doesn't have that much leeway to raise rates if it wants to avoid hurtling over the cliff and into a big recession

The Fed is in a similar situation. It's trying to steer a course between the twin evils of inflation and recession. If it keeps rates too low for too long, the economy will start to overheat, and inflation will get out of control. If the Fed raises rates too quickly, it'll tip the economy back into recession. So it's true that at any particular instant, the Fed can make interest rates go up and down. But the Fed doesn't have that much leeway to raise rates if it wants to avoid hurtling over the cliff and into a big recession.

The European Central Bank did exactly that when it raised interest rates prematurely in 2011. That proved to be a huge mistake, because it tipped the eurozone economy into a double-dip recession. Countries like Greece and Spain are still feeling the pain today.

A key thing to notice here is that the ECB didn't just damage Europe's economy with its interest rate hike, it wasn't even able to keep interest rates up for very long. Before the end of the year, it became obvious that the higher rates were hurting the economy. The ECB was forced to reverse itself and return interest rates to their previous level. Today rates are even lower than they were in 2011, and that year's premature interest rate hike is part of the reason.

So if you want higher interest rates in the long term, you should be rooting for the Fed not to make the ECB's mistake. Low rates accelerate the economy, getting us more quickly to a point where the economy is healthy enough that private demand for capital pushes rates upward.