What was going on when I was born?

The index of leading economic indicators, which the Government uses to project the economy's performance six months or a year ahead, showed a sharp decline of nine-tenths of 1 percent in June, the Commerce Department said today. The index is notoriously volatile, subject to revisions that can show it moving in the opposite direction from the one first reported. But the steepness of the decline reported today appeared to confirm a trend toward slower expansion that has been reflected in the index since spring. Analysts expressed relief that the heated economic growth of the last 19 months appeared to be cooling. ''We need a report like that,'' said Morris Cohen, an economic forecaster in Hackensack, N.J. ''Everybody's been saying we need a slowdown. And, lo and behold, here's the evidence.''

The United States men's gymnastics team, alternately cautious and daring, won the team gold medal in tonight, upsetting the reigning world champions from China. ''This is certainly comparable to the U.S. hockey team winning the gold medal in 1980,'' said Abie Grossfeld, the team's head coach, as a near-capacity crowd of 9,356 at Pauley Pavilion waved American flags and chanted ''U.S.A.! U.S.A.!'' behind him. The startling victory capped a day of competition in which the United States continued to dominate swimming, winning all five finals including a victory by Rick Carey of Mount Kisco, N.Y., in the men's 200-meter backstroke. The United States also won a gold in shooting as 18-year-old Pat Spurgin of Billings, Mont. took the women's air rifle competition. The Americans won seven gold medals yesterday to bring their total to 16 gold - 11 in swimming - in three days. In addition, the American men's and women's basketball teams looked impressive in winning their second games in the round-robin competitions.

The Champion International Corporation and the St. Regis Corporation announced jointly yesterday, as exp ected, that they had signed a definitive agreement to merge the two big paper companies in a deal valued at $1.7 billion in cash and stock. The merger would create the nation's biggest paper producer in terms of sales, far outstripping the Georgia-Pacific Corporation, the current leader. It would also challenge the International Paper Company for the top spot in the industry in terms of pulp and paper tonnage produced. Reflecting typical takeover patterns, Champion stock fell $1.875, to $17.25, on the New York Stock Exchange. St. Regis shares closed at $49.875, off a slight 37 1/2 cents.

The Champion International Corporation's proposal to acquire the St. Regis Corporation would create the nation's largest forest products company, and, analysts say, set the stage for an expected flurry of mergers and acquisitions in the industry. Nevertheless, Champion's move brought mixed reactions from Wall Street. Some analysts saw it as aggressive and gutsy, putting Champion's chips strongly in the paper industry and lessening its reliance on the cyclical building-products industry. Others questioned the deal's financial structure, noting its debt load for Champion and saying that it would dilute the value of Champion's stock. Business benefits from the combination might not materialize for a few years, they said.

The International Business Machines Corporation yesterday announced bonuses for both investors and customers. The electronics concern gave its first dividend increase in 15 months and said owners of its much-criticized PCjr home computer could get a new keyboard free. Analysts said the dividend increase, from 95 cents a share to $1.10, was surprising but reflected I.B.M.'s strong profits. The company's sales this year have exceeded the forecasts of many analysts.

A picture caption in Metropolitan Report last Wednesday with an article about the Mini-Bravettes, a girls' softball team in Brentwood, L.I., misidentified the player holding a glove over her face. She was Melissa Alvarez.

Leaders of striking hospital workers in New York City angrily rejected a proposed 4 percent wage increase yesterday and warned that they would take stronger measures on picket lines to achieve a better settlement. ''Do not mistake our passiveness with weakness,'' said Gary Maio, a union delegate, as he and other strike leaders ended their first formal negotiating session with hospital administrators by shouting them out of a second- floor meeting room at the Roosevelt Hotel. The delegates unanimously rejected the offer of a 4 percent increase in each year of a proposed two-year contract. Later, the offer was put to a membership vote that began last night at the Felt Forum at Madison Square Garden.

Employees refer to the black cloud that hangs over the company. Or an executive might mention how well everything is going for the A. H. Robins Company, and then add, ''Except for that one thing.'' That one thing is the Dalkon Shield, an intrauterine birth-control device that the company hasn't made for a decade but that continues to haunt it. One of the most tainted names in the annals of consumer products, the Dalkon Shield was touted for its exceptional reliability in preventing pregnancy. But thousands of women who used the plastic oval suffered infections, sterility and septic abortions (badly infected miscarriages) that they say stemmed from the Shield. The device has been blamed for 21 deaths.

WEDNESDAY, AUGUST 1, 1984 The Economy The index of leading economic indicators fell 0.9 percent in June, the first decline in 21 months. Economists welcomed the report as a sign that the economy is moving to a more sustainable rate of growth after two quarters of fast expansion. The index, a barometer of the economy's future performance, is volatile, however, and subject to revision as later data come in. (Page A1.)

''Anybody who's wise enough to pick Mario Cuomo to give the keynote address and smart enough to pick Geradline Ferraro for Vice President should be the next President of the United States.'' - Walter F. Mondale (A1:2.)

AS recently as 10 years ago you would rarely find a young American chef stirring sauces, basting the poultry and tending the pantry in any of the country's top restaurants. Almost every restaurant of national reputation that offered serious dining was staffed by chefs born abroad. In the last five years, however, young American-born chefs have begun to take their places in the kitchens of fine restaurants in many parts of the country. Not only are many of them proving to be superior cooks, they are also making contributions to a distinctly American cuisine. This striking change came to mind a month or so ago when I stopped for a meal at one of the most stylish hotels to open recently in this country, the Campton Place in San Francisco. The graceful dining room is small (there are accommodations for only 68 guests), but the china is Wedgwood and the crystal and silver impeccable. But what really struck me was the American character of the menu: Among the selections were grilled salmon with a timbale of zucchini and grits, pan-fried brook trout with black walnuts, veal medallions with farmer cheese and fresh basil, a rabbit soup with barley, Missouri ham with papaya and lime, and an omelet with Illinois brie cheese. The food, start to finish, was a delight. The corn sticks that accompanied the meal were the best I have ever sampled.

The American Telephone and Telegraph Company yesterday received a 15-year, $43 million tax abatement from New York City on its new Madison Avenue headquarters. The city's Industrial and Commercial Incentive Board, in a 6-to-1 vote, granted the abatement after getting assurances that the company would put a communications museum into a completed three-story annex behind the building. Earlier this year, A.T.&T. officials said that, rather than keep a commitment to the City Planning Commission to create a free public museum, the company would use the annex predominantly for internal needs.