At the annual Gridiron Club dinner last weekend, White House chief of staff Donald T. Regan produced some witty, self-depreciating (if ghost-written) lines designed to show that he is a regular guy after all.

"Hey, I'm not always sure of myself," Regan began. "I have moments of anxiety. In fact, many of us in the administration are very anxious about the outcome of an event so important it will determine our place in history. No, not the arms talks -- David Stockman's book."

Predictably, it was good for a laugh. But one doesn't have to be very Freudian to believe that the Reagan administration is beginning to worry about its place in the history books.

And one shrewd observer of the Washington scene, Lester R. Brown of the Worldwatch Institute, thinks that unless the president abandons the arms race with Russia, history won't remember him for anything positive, but only for doubling the national debt and losing the race for economic power to Japan.

Brown's sober note, which would not have brought any smiles at the Gridiron, becomes all the more poignant in the wake of Reagan's macho adventure in the Libyan Gulf of Sidra. If Reagan and his right-wing advisers are interested mainly in flexing American military muscle, we can forget about regaining economic leadership in the world.

Worldwatch is a small think tank, which Brown started 10 years ago, concentrating on such basics as erosion of the environment, the population explosion and Third World misery. His annual evaluations of the state of the world have gained increasing attention, even to the point of a flattering review of his current volume by conservative Hugh Sidey in a recent Time magazine column.

In an interview this week, Brown called attention to the fact that when Philippine President Corazon Aquino needed technical assistance to recover from the devastation of the Marcos years, she turned to Japan, not -- as once might have happened -- to the United States.

This, he suggests, is one tip-off to the rise of Japan's economic power at the expense not only of the United States, but of the Soviet Union too. Both superpowers have been engaging in a costly arms race. While we and the Russians have been spending our wealth and best scientists on arms -- and have become the big arms exporters as well -- Japan has become the big exporter of consumer goods. Before the end of the decade, he notes, Japan will slip ahead of the United States as the world's No. 1 trading power.

In stressing Japan's advantage in being out of the arms race, perhaps Brown oversimplifies the problem. As management consultants James Abegglen and George Stalk Jr. point out, superior manufacturing and management techniques yield Japanese companies cost advantages in the range of 30 percent over Western competitors (before considering exchange rates). "The advantage is unbearable," they say.

There are other reasons for Japanese success: better employer-employee relations; aggressive company efforts to gain shares of the world market; and an exceptional educational system. Thomas P. Rohlen of the University of California reported in a 1983 study that the "average Japanese high-school graduate has the equivalent basic knowledge of the average American college graduate."

But all of these advantages of the Japanese are multiplied, in Brown's view, by the American preoccupation with building up the military establishment. In "State of the World 1986," Brown says: "Japan, initially barred from the international arms race, now has mastered the new geopolitics, recognizing that in the nuclear age, military power is of limited value, and that political influence derives more from the economic strength of a highly productive, internationally competitive economy."

Brown argues that the superpower arms race has sapped the energies of both Russia and the United States. Reagan has presided over the doubling of the national debt from about $1 trillion when he came into office to $2 trillion now. Our huge budget deficits triggered high interest rates and a resultant swelling of Third World debt. The banking system is shaky, and Brown points out that a portion of the $213 billion farm debt -- like Third World debt -- will never be repaid.

The Russian economy, meanwhile, is already on the rocks, producing 20 percent less grain than in the 1970s; its sophistication in computers reportedly lags behind that of Brazil and South Korea. Except for arms, almost nothing the Soviets produce is competitive with what the West can offer.

Brown's bottom line: unless Reagan and Gorbachev quit thinking of security in traditional military terms, they will cede even more power to Japan. It should be a sobering thought, especially if the two leaders are interested in what the history books will say.