Years ago, in the era of silent films, serial movies flourished. The most successful and best known was the Perils of Pauline starring Pearl White, who one week would be strapped to a wagon pulled by runaway horses, the next week she'd be lying on a railroad track as a loco motive bore down on her, the following week she might be in a sinking boat or in a house enwrapped by fire. Always a rescue took place, always she escaped from the seemingly inescapable.

Nowadays, we have an analogy: The perils of Paul A. Volcker and how the chairman of the Federal Reserve System has escaped from dire economic peril without precipitating the nation into a long, deep, and debilitating depression.Inflation was a clear and persistent Paul Volcker peril from 1977 into 1982. The fee banks charged their best customers got up to more than 20 percent. That has now dropped to 7 1/2 percent. And yields on long-term government bonds, once 13 percent and 14 percent, are now down to 7 1/2 percent . It required two back-to-back recessions - 1980 and 1981-82 - to escape from those perils. Mr. Volcker escaped from the peril finally but not the criticism.

The budget deficit - out-of-control expenditures relative to receipts - has become a perpetual peril from which Mr. Volcker gets no relief. The deficit threatens to rise to $220 billion, and neither President Reagan nor Congress have been willing to confront it directly by raising taxes. The Gramm-Rudman-Hollings Act is an effort at deficit reduction, but its effectuality has yet to be demonstrated.

The dollar. That's an up and down Paul Volcker peril. It's linked to another peril: The U.S. trade deficit. The excess of U.S. imports over exports could exceed $180 billion this year. In Mr. Volcker's words, such a deficit is ''unsustainable." It means the United States is living beyond its means and is going into debt to do so.

To alleviate this peril, Mr. Volcker has called on West Germany and Japan to boost domestic consumption - increase "home demand." If Germans and Japanese "live it up a bit" they might buy more from the United States. That would increase U.S. exports. At the same time, because domestic business improved, the sales of German and Japanese manufacturers at home would rise. Therefore businessmen would be under less pressure to export. So their sales - their competition in the U.S. market - might decrease. That would tend to lower the U.S. trade deficit.

Once, this country was the world's dominant creditor nation. It is now a debtor nation. Foreign ownership of U.S. securities and other assets exceeds U.S. ownership of foreign assets. That reduces the U.S. balance of payments. It decreases the net income derived from investments overseas.

To satisfy foreign investors - to keep them happy holding dollar assets, such as U.S. Treasury securities - interest rates here have to be higher than what foreign investors can earn at home. But U.S. interest rates must not be too high. That's another peril of Paul.

High U.S. interest rates would be doubly dangerous. They would discourage U.S. businesses from borrowing and embarking on new undertakings. That would be detrimental to business and would prolong the country's economic doldrums.

High interest rates also would imperil nations struggling to meet payments on oversized indebtedness - Brazil, Argentina, Mexico and so on. To diminish this peril, Secretary of the Treasury James A. Baker III and Mr. Volcker have labored to persuade the International Monetary Fund, World Bank, and commercial banks to make loans, reschedule debts and lower interest rates.

Pauline had this advantage over Paul. She went from peril to peril, but at the end of the serial, her perils were over and she could live happily after. The perils of Paul persist. The budget deficit remains, the trade deficit gets bigger, inflation might surge again if the Federal Reserve tries to keep interest rates low while pumping up the money supply to finance the bulbous U.S. budget deficit, and the dollar remains a perilous quandary: What's the right price for it?

If it's too high, U.S. exporters are hurt. If it's too low, U.S. consumers are hurt. So Paul is beset. Solve one peril and get another. And, then there's the ultimate peril: Recession

Mr. Volcker and his colleagues on the reserve board have been lowering interest rates. Theory: Easy, low-cost credit stimulates borrowing. It encourages businessmen to expand and consumers to spend; it should bring about the promised pickup in the economy.

But will it? If it doesn't, like Reserve Board Chairman Marriner S. Eccles in the 1930s, Mr. Volcker will be criticized: What's wrong? And he may have to answer as Mr. Eccles did: If people don't want to borrow, making money cheap and credit plentiful is like pushing on a string.

Recession is the peril of all - President Reagan's, yours, mine, and everyone else's, and let's not leave out Paul. The perils of Paul are a continuing, never-ending serial unlike Pauline's.

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