For Bagehot, “the natural system” was the one “which would have sprung up if Government had let banking alone.” There would have been “many banks of equal or not altogether unequal size.” He described this as “the many reserve system,” in which each bank held reserves for itself, which he believed would have meant a stronger banking system. In modern parlance, Bagehot’s celebrated “lender of last resort” is a second‐​best solution—second to a world of competitive banks and no central bank.

In the post‐​Civil War era, the U.S. banking system did not operate as Bagehot’s “natural system.” Government regulations concentrated bank reserves in major cities, with the result that the economy was subject to panics and bank runs (which were rare in other countries), culminating in the Panic of 1907. Instead of fixing the problems of the national banking system, however, lawmakers led by the progressive president, Woodrow Wilson, created a central bank, the Federal Reserve System.

A third myth is that of central‐​bank independence. In the U.S., the Federal Reserve is viewed as having gained independence as the result of the Accord of 1951 with the U.S. Treasury. After the accord, the Fed was no longer required to maintain the prices of government bonds and thus fix interest rates. That requirement, born of the fiscal needs of World War II, hindered the Fed from fighting inflation by preventing it from raising interest rates during the Korean War.

Since 1951, there has been no relevant change in the Fed’s legal status. The bank has acted independently at times—but at other times its actions have been anything but independent of the other branches of government.

In the 1950s, under Fed Chairman William McChesney Martin, inflation remained low. Yet his had little to do with Martin. President Eisenhower was an inflation hawk, and throughout the 1950s budget deficits were low or nonexistent. Once Presidents Kennedy and Johnson accepted Keynesian fiscal activism, deficits rose. Martin was happy to accommodate the government with easy money. He did not believe monetary policy could—or should—operate independently of fiscal policy. What followed was the first peacetime inflation in U.S. history.

The Fed’s independence hit a nadir under Chairman Arthur Burns. The diary he kept during the Nixon years confirms that Fed policy became subservient to administration goals and the president’s re‐​election campaign. As he wrote in one diary entry, he told Nixon that “I was looking after monetary policy and he did not need to be concerned about the possibility that the Federal Reserve would starve the economy.” The great inflation of the 1970s was the outcome.

Paul Volcker, chairman from 1979 to 1987, restored the Fed’s inflation‐​fighting reputation, and the bank under his management is held up as a model of independence. And true enough, there were many in the legislative branch, as well as outside the government, who complained bitterly about his tight‐​money policy, which ultimately reined in inflation and spurred growth. Even so Mr. Volcker, like Martin before him, had strong support from the two presidents during whose administrations he served, Jimmy Carter and Ronald Reagan.

If we fast forward to today, it is difficult to portray the Fed under Chairman Ben Bernanke as operating independently in any meaningful sense. In 2011, the Fed purchased an unprecedented 77% of Treasury debt. With his long‐​term commitment to ultra‐​low interest rates, Mr. Bernanke has hitched monetary policy to the fiscal policy of the Obama administration in a bid to inflate asset prices. That is the opposite of what is supposed to be central bank independence—and places the Fed closer to a presidential administration than it has been since the days of Burns and Nixon.

The lesson from this history is what I call “central banking without romance,” after a famous article by the late Nobel prizewinning economist James M. Buchanan, “Politics Without Romance.” A central bank is necessary as long as an economy is wedded to a fiat currency. And it may at times behave independently—but not in the face of large‐​scale budget deficits, as we have today.

Pursuit of price stability is the one goal that nearly everyone agrees is a central bank responsibility. Yet it is the one on which the Fed and other central banks have failed miserably. Since the Fed’s founding in 1913, consumer prices have increased by a factor of 23 times. If the U.S. can extricate itself from fiscal deficits, price stability would be an attainable goal for central banks. Otherwise, central banking is nothing but mythology.