What was going on when I was born?

Despite surprisingly steady business signals in January, many corporate economists expect sluggish economic activity in the United States through the first half of 1981. But they see the economy picking up in the second half, building toward a robust 1982. While most rousingly endorse the combination of Federal budget reductions and tax cuts for businesses and individuals that President Reagan is expected to propose Wednesday, they stress that such a balm for past economic wounds will not work much cure for several months. The economists say that Federal Reserve Board policy toward interest rates and money supply growth will play a large role in determining the path of the nation's economy for the rest of the year.

While Adelphi University students mourned a classmate who was shot and killed yesterday by a Garden City policeman, the Nassau County police said that a grand jury investigation of the shooting would begin this week. As students gathered today outside the Ruth S. Harley University Center, several disputed the police version of the incident. They said they hoped the grand jury proceeding would clarify what had actually happened. According to the county police, the officer, John McNulty, fired his revolver after Edward Fonseca grabbed his blackjack and lunged at him. The .38-caliber bullet severed two of Mr. Fonseca's arteries, pierced his liver and then came to rest in his stomach. He died three hours later at Nassau Hospital in Mineola.

Vice President Bush and some key members of Congress urged support today for the budget package that President Reagan plans to present to Congress Wednesday, but representatives of groups fearing that they could be hurt urged caution in reducing government spending. Saying in New York that the Federal budget had too much ''fat,'' Mr. Bush added: ''We can and will be able to reduce the heavy burden of taxation on our people - taxation that stifles industrial growth and individual initiative.' And Senator Pete V. Domenici, Republican of New Mexico, chairman of the Senate Budget Committee, said that Mr. Reagan's proposals would bring inflation down to ''a reasonable level'' by 1984 if Congress approved the President's whole package of $48 billion in cuts in this fiscal year and the next. Opposes 'Piecemeal' Work ''The real test will be whether it can be kept together during the legislative journey,'' Mr. Domenici said. ''It is important that it not be cut up piecemeal by various Congressional committees.''

The chairman of a committee of the Taxi and Limousine Commission that this week will consider a 50-cent surcharge for nighttime taxi rides in New York City said yesterday that the charge would not be approved unless the commission could obtain accurate income reports from all segments of the taxi industry. The committee chairman, Marvin Greenberg, said the financial records would have to be reviewed and public hearings would have to be held. He said it would be at least several weeks before the full commission would act on the surcharge proposal.

''When you start manipulating a system that treats three million people a day you'd better be a little careful before jumping off the cliff.'' - Dr. James H. Sammons, executive vice president of the American Medical Association, speaking of proposals to cut Medicare and Medicaid. (A12:3.)

An article in The Times yesterday gave an incorrect starting time for a ground test of the space shuttle Columbia. The rehearsal countdown is now scheduled to begin at 7:15 P.M. today. Article on Page A10.

Its customer list bore the names of Jacqueline Kennedy Onassis, Farah Diba and Leah Rabin, wife of the former Israeli Prime Minister, among others. But a few weeks ago, Beged Or, Israel's most famous fashion house and one of the finest leather couturiers in the world, found itself in the midst of ignominious times. After two years of financial difficulties, a commercial court sold Beged Or, whose name is Hebrew for ''leather clothing,'' to the nation's largest textile exporter, a modern industrial complex committed to mass production and large-scale exports. Polgat Enterprises, a publicly traded group with $70 million in exports, bought bankrupt Beged Or for $1.6 million, according to Chaim Pollak, a Polgat board member and managing director of Bagir, one of the group's subsidiaries.

When Governor Carey came here recently to encourage Japanese companies to invest in New York State, one of the few plant tours he took was at Okuma Machinery Works. Okuma already has a wholly owned subsidiary, mainly a sales and distribution office, in Farmingdale, N.Y., the first United States operation for the Nagoya-based machine tool maker. Like some other Japanese machine tool companies, Okuma started its American operation to help head off possible trade friction, similar to that now faced by Japanese auto makers over exports to the United States. Machine tools, simply put, are machines that make the parts for other machines. They comprise a multibillion dollar market in the United States, and models range from hand-operated devices that shape and plane metal to sophisticated computer-linked systems that build robots.

Steve Allen is signing some letters at the same time as he is skimming a manuscript at the same time as he is getting ready to utter a thought into a tape recorder. Before he can polish all that off, a script for a benefit is dumped on his desk. Then a letter arrives confirming that he is to appear with the Milwaukee Symphony. He shakes his head, emits his familiar ''heh-heh-heh'' laugh, reaches up to straighten his glasses. ''I think it would be appropriate after I die,'' he says, ''if they just shovel 8,000 pounds of paper on top of me instead of dirt.'' Working out of paper-strewn offices here on busy Burbank Boulevard, Steve Allen is a virtual one-man media conglomerate. His versatility qualifies him as a personal hedge against the uneven nature of the sundry entertainment businesses. If a television series is out of favor with the Nielsen ratings, there's always song-writing. If the book business is sluggish, there's always the nightclub act.

The failure of last month's guerrilla offensive against El Salvador's civilian-military junta has led several governments and political parties in the region to reconsider their previous unconditional support for the country's Marxist-led Democratic Revolutionary Front. The front, a coalition of Marxist guerrillas, Social Democrats and dissident Christian Democrats, for the first time has come under strong pressure from its traditional allies to seek a political solution to the conflict. ''Until the guerrillas and the junta had tested their strength, there wasn't much to be discussed,'' said a Latin American diplomat who now is trying to promote a negotiated settlement. ''Now, after the failed offensive, we all have to look at the situation with fresh eyes.''

The St. Louis Blues, despite a penalty-filled second period in which they yielded three goals, triumphed over the Rangers last night, 5-4, at Madison Square Garden. The victory, coming after ties with Buffalo, Montreal and the Islanders on a six-game trip, moved the Blues into first place over all in the league. They have 80 points, 2 more than the Islanders, who did not play. It was also the third time the Blues had beaten the Rangers in three meetings.

The three railway refrigerator cars were drawn up today on a siding that is normally used for grain exports. A handwritten sign on the first of them identified their contents. ''Corpses,'' it said. A small crowd gathered in the early morning sun. They were waiting for a chance to search for brothers and sons who might have perished in the spasm of devastating combat that started here last week with clashes between factions of former guerrillas tied to the two political parties in Prime Minister Robert Mugabe's Government.