Three separate government reports released yesterday offered firm evidence that the economy is beginning to slow, and a top Treasury official said the government expects two quarters of economic decline before the benefits of its economic program are felt.

"You can't get the longer-run benefits without short-term pain," Beryl Sprinkel, Treasury undersecretary for monetary affairs, said yesterday. He also said that work has begun on the administration's promised second tax bill which was to include various congressional tax-cutting favorites.

But Sprinkel said this would be ready around Christmastime, rather than in the midsummer as the administration had suggested before. It is more likely that Congress will try to put the additional measures into the first tax bill, rather than wait for a promised second bill, for which there is no money allocated in Reagan's figures, Capital Hill sources have said.

In addition, yesterday a flood of major banks followed Citibank, the nation's largest, in dropping the prime rate to 17 1/2 percent. A handful of large banks already had moved to the 17 1/2 percent level, which now becomes an industrywide benchmark.

In the first of yesterday's three reports, the Federal Reserve Board said that industrial output fell by 1/2 percent last month, the first drop in mor than six months. At the same time, personal income grew by only 0.7 percent, probably not enough to compensate for rising prices during the month, and housing starts plunged dramatically by 24.6 percent, the Commerce Department reported.

Economists have been predicting some slowdown in growth this year, with a drop in the nation's gross national product (the total value of all goods and services produced in the United States) during at least one quarter of this year expected by many, although not all, analysts.

Last year's strength in the economy apparently continued into January, but many have trailed off in the last few weeks, experts believe. The economy as a whole almost certainly will show a positive GNP number for the January-March quarter, with any downturn beginning in the second quarter, they say.

The economy appears to have been slowed by the sharp credit squeeze late last year, as the Fed pushed up interest rates and moved to slow money growth. The money supply now has come back within target, and interest rates are slipping as loan demand eases. This drop in interest rates may help to cushion the economy's slowdown.

Economist Otto Eckstein hailed the economic slowdown as "the first time ever in modern history that the Federal Reserve has managed to slow down money growth without provoking a credit crunch. It is the first orderly return of money aggregates to their targets."

Interest rates are expected to go on falling for the next few months, although there is much dispute over the accuracy of administration forecasts of a sharp and prolonged fall in interest rates.

Industrial output rose by only 0.4 percent in January, the Fed reported yesterday, down from the original figure of 0.6 percent. The December rise was 1 percent. February production is 1.2 percent below the February 1980 level.

One reason why the economy has gone on growing for a longer time period than expected is that people have dipped into savings to keep up their spending. Last month personal consumption rose by 1.3 percent, or $23.2 billion, while income went up by only 0.7 percent, or $14.9 billion after seasonal adjustment. This followed a rise of 1 percent, or $22.2 billion, in January.

Retail sales have risen strongly in January and February, with new figures yesterday showing a revised sales growth of 1.1 percent last month. Savings must have reached a record low, Eckstein said.

But this decline in savings is unlikely to go on for very long. There is as limit to how much lower the proportion of income which is saved can fall. Private wages and salaries rose just 1/2 percent in January. Factory payrolls were up by 0.6 percent, after seasonal adjustment, following a 1 1/2 percent increase in the previous month.