Easy money is driving up the price of stocks, bonds, houses and other assets in a era without historical precedent.

Janet Yellen’s comment last week at the International Monetary Fund headquarters in Washington, D.C., that stock prices are “quite high” hardly captures the frothiness in U.S. financial markets. The Federal Reserve chair’s admission also stopped short of acknowledging the role of free money in inflating the price of stocks—as well as the price of bonds, houses and every other financial asset.

At Morgan Stanley Investment Management, we have analyzed data going back two centuries and found that until the past decade no major central bank had ever before set short-term interest rates at zero, even in periods of deflation.

To critics who warn that pumping trillions of dollars into the economy in a short period is bound to drive up inflation, today’s central bankers point to stagnant consumer prices and say, “Look, Ma, no inflation.” But this ignores the fact that when money is nominally free, strange things happen, and today record-low rates are fueling an unprecedented bout of inflation across asset prices.

The Fed’s defenders quibble that houses are less pricey than in the bubble of 2007, or that stocks are less pricey than in 2000, which misses the difference this time around. In the past 50 years, valuations of U.S. stock prices have been higher than they are now for less than 10% of the time, and similar figures hold for bonds and houses. This kind of synchronized boom has never happened, not even before the last two major meltdowns. My research team’s composite valuation for the three major financial assets in America—stocks, bonds and houses—is currently well above levels reached during the bubbles of 2000 and 2007.

Faith in the Fed’s easy-money policies has encouraged a dangerous complacency. The mantra on Wall Street is that good economic news is good news for the markets, but that bad news is also good news, because it will encourage the Fed to keep rates lower for longer. This has led to one of the longest rallies the U.S. stock market has ever experienced, without even a 10% correction. Returns since 2012 are the highest for any three-year period in recorded history, after adjusting for the risk of holding stocks.

The Fed’s approach has spread to central banks in Europe, Japan and China, creating a new world in which investment decisions are guided by the availability of easy money, not opportunity. Over the past three years, global stock prices have risen rapidly despite tepid economic growth. Oh well, the central bank responds: We target consumer prices, not assets.

This job description is outdated, because the task is largely done. In emerging nations, the average annual growth of consumer prices now hovers around 5%, down from a peak of 116% in 1994. Add in the rich countries, which are generally more stable, and global inflation has fallen to 2% today from near 20% in the early 1970s.

Central bankers are still fighting to control consumer prices, only now for the opposite reason. Rather than raising interest rates to contain consumer spending and inflation, they hold rates down to encourage spending and induce inflation, because the global inflation rate of 2% is dangerously low in their view. The fear is that slowly rising prices will tip into falling prices. The boogeyman is not hyperinflationary Germany of the 1930s, but deflationary Japan of the 1990s, when the country fell into a downward spiral of falling prices, weak demand and stagnant growth.

Japan taught the world two lessons: that consumer price deflation is bad for growth and that it is hard to shake. Both are inaccurate. Before World War I, many nations experienced deflation, sometimes driven by weak demand and leading to weak growth, but as often driven by rising productivity and accompanied by strong growth.

A recent Bank for International Settlements study on the postwar period found that long bouts of deflation were exceedingly rare, but short bouts were common. More important, average annual GDP growth was roughly the same regardless of whether prices were rising or falling. The upshot: Consumer price deflation is not necessarily bad for growth.

One problem is that the world changed faster than the Fed. Trade has jumped to 60% of global GDP from 40% in 1980, and increasing competition puts downward pressure on consumer prices. The forces of expanding supply from China to Mexico are pushing the global average inflation rate down to a level that looks scary low only when compared with the 1970s highs. In fact, consumer price inflation is still above the long-term average, dating to the year 1200, which is 1%.

But global competition wields the opposite effect on asset prices. The opening of financial markets means that many more buyers are bidding up prices for stocks in New York, or real estate in Miami or bonds in Chicago. The result is that central banks are unleashing easy money to fight an imaginary villain, consumer price deflation, at the risk of feeding a real monster, asset price inflation.

Every major economic shock in recent decades has been preceded by an asset bubble: housing and stocks both before Japan’s meltdown in 1990 and before the Asian financial crisis in 1998; stocks before the U.S. dot-com bust in 2000; housing again before the crisis in 2008. Strikingly, even as asset prices were climbing before the busts of 2000 and 2008, the Fed kept monetary policy loose because consumer prices were rising only moderately. That is the same excuse we hear now, amid a price boom in stocks, houses and bonds.

It is true that bubbles are most dangerous when people are borrowing heavily, and are buried by debt when the bubble collapses. Because U.S. households have been cutting debt, Ms. Yellen says the situation is not unduly risky. But U.S. corporations are borrowing heavily, and not all bubbles are fed by rising debt.

The Fed now leads a culture of central bankers who see their job as reducing unemployment and stabilizing prices for consumer goods only, come what may in the markets. This needs to change. In a world in which high trade and money flows tend to restrain consumer prices but magnify asset prices, central banks need to take responsibility for both. After all, asset price inflation is as dangerous as consumer price inflation.