New York — New York City may be on a fiscal roller coaster for many years to come.
Just a year ago, officials were proclaiming the city had entered a ''new era'' of financial stability. And, on the surface, many of the problems that pushed the nation's biggest city to the brink of bankruptcy in the late '70s looked as if they had been addressed.
But, according to a cross section of fiscal and economic experts inside and outside of city government, that brink is still just a step away. Enough safeguards are in place to make it more difficult for the city actually to go bankrupt but, in the words of one expert, the city will be leading a ''hand-to-mouth existence'' for many years. And essential services will remain just that: ''essential,'' basic, patched-up instead of redrawn and replaced.
Officially, at least, Mayor Edward I. Koch, the man chiefly responsible for putting the city on sounder financial footing, is committed to doing everything in his power to curb expenses and balance the city budget. In fact, New York state law now requires him to balance the budget, in line with ''generally accepted accounting principles'' used in the private sector.
Before Mr. Koch took office five years ago it seemed New York City would sometimes ''balance its books with blinders on,'' as one political pundit put it. The city often used money in the capital budget to pay operating expenses. Overestimates of revenue became a yearly ritual.
At present, a complex set of proposed tax increases, municipal employee layoffs, and further delays in badly needed capital improvements is being hammered into place. It is hoped these will bridge what the mayor's own analysts expect to be a $1.3 billion budget deficit for fiscal year 1984, which begins July 1, l983.
Behind these deficit forecasts lies some fiscal blunders committed between Koch's early commitment to setting the city's affairs in order and his unsuccessful 1982 gubernational bid.
The biggest of these, according to experts, was the city's wage settlement with organized labor in the fall of 1982. At a time when the battle against inflation was starting to be won on the national level, New York municipal workers received their most generous two-year salary package in nearly a decade.
''For the first times since the fiscal crisis of 1975, a newly negotiated municipal labor settlement provides for percentage increases in base salaries which are greater than the forecast rates of inflation,'' says a recent Citizens Budget Commission report on the city's budget prospects concludes. The CBC is a private, nonprofit organization which keeps close watch on city finances and services. ''The agreement with nonuniformed employees provides fiscal year 1983 raises of 8 percent (effective September 1983) and fiscal year 1984 raises of 7 percent, and the agreement with uniformed employees provides 8 percent for both years.''
Koch critics, such as City Comptroller Harrison Goldin, say the generous wage package was an olive branch to organized labor. Indeed, Koch was desperately trying to gain labor's support - he failed to get most of it - and lost the gubernatorial primary largely because of labor's opposition.
While the mayor has denied the wage agreeement was tied to politics, it certainly is tied to the city's financial health for a long time to come. CBC has recommended that the administration renegotiate the agreement.