Aided by a District government subsidy estimated by Mayor Marion Barry at $2.4 million, a New York life insurance company owned by labor unions has bought a tract of city-owned land near Capitol Hill and begun construction of an office building for its new headquarters.

The eight-story building, onMassachusetts Avenue between 2nd Street and New Jersey Avenue NW., will be the new home of The Union Labor Life Insurance Co. Barry, who presided at groundbreaking ceremonies last week, said the subsidy, in the form of a write-down on the price of the land, was justified by the "high quality" development that will bring "jobs and revenue" to the District.

The company will move all of its headquarters operations from New York to the District, and has asked its employes to make the move. Barry said that the move will bring "750 permanent jobs for D.C. residents and 1,500 permanent jobs in all," a needed shot in the arm for a city economy jolted by the death of The Washington Star and by a recent consultant's report showing that many businesses are planning to move out of the District.

The Redevelopment Land Agency, the city's Urban Renewal organization, sold the 35,336-square-foot parcel for $2.1 million, or $59.43 per square foot. The selling price, which was approved by the RLA board last December, was the value set by an independent appraiser in September, 1979, before the prices of downtown land began to take off.

The actual sale contract was completed July 21. Regulations of the U.S. Department of Housing and Urban Development normally require that land be reappraised before sale if the appraisal is more than 18 months old. City housing department officials, who have been criticized by citizens' groups and city council members for undervaluing urban renewal land, said they were within the HUD time limit because the Board vote was taken last December.

Union Labor Life is a relatively small insurance company. Its assets of $812.7 million and its $4.5 billion of insurance in force in 1980 do not place it among the top 100 companies. But it is an innovative organization, branching out into pension management, securities and mortgages, and its reported income last year was $479.9 million.