Barely has a recession been as eagerly awaited as this one, nor as carefully nurtured by an administration. Presidential encouragement for this year's economic slowdown was, on the face of it, all the stranger since 1980 is an election year.

The reason for this reversal of traditional election-year wisdom is not that hard to find, however. Inflation, as measured by the consumer price index, soared early this year to an annual rate of about 18 to 20 percent. This was a sharp increase as compared to the underlying 8 to 9 percent rise a year earlier. By spring the consumer boom that was sustaining economic growth appeared to be both fueled by, and fueling, spiraling prices.

President Carter and his advisers, along with many other people in the nation, felt that high and rising inflation was a greater evil than increased unemployment and recession.

The president and his advisers are obviously still concerned about inflation. But their enthusiasm for the recessionary cure has cooled. The short-term goal of Carter's new economic policy, announced Friday, is to speed the recovery and get people back to work, although the longer term aims are to continue to fight inflation and to try to raise productivity.

The administration's belief that new measures will be needed to bring the economy securely out of recession is based on forecasts that the recovery, left to itself, would be very slow, and would do little to bring down unemployment next year.

When the 1980 recession finally came in the second quarter of this year, it hit surprisingly hard. The 9 percent -- computed on an annual basis -- fall in output between March and June almost matched the previous post-war plunge in the gross national product in 1975.

Unemployment jumped very sharply meanwhile. An additional 1.7 million people joined the jobless ranks in just two months this spring, pushing up the rate to 7.8 percent of the labor force in May from 6 1/4 percent in March.

But forecasts of a 9 percent unemployment rate by the end of the year now looks too high. Although private forecasters generally agree with the official view that the recovery will be slow and unemployment will remain high without some tax cuts next year, there are numerous signs that the economy began to move out of recession this summer -- much sooner than expected.

Friday's record jump in the leading indicators for the economy was the latest of these signs. It follows reports of a marked recovery in both the housing and the auto markets: two of the hardest hit by this recession.

But it is also clear that inflation has remained historically very high, despite the economy's sharp slowdown. Carter emphasized in his statement Thursday that "inflation has fallen sharply" in recent months. Asked to say just how sharply, administration officials later described the present underlying rate of inflation at about 9 percent.

That is considerably lower than the rate shown by the consumer price index in the first few months of the year -- when the economy was growing strongly -- and it is significantly higher than towards the end of any previous recession.

As recovery picks up, inflation is more likely to move up than slow down further. The recent rise in the prime rate is a sharp indication of the fear in financial markets that inflation has bottomed out and will quickly begin to speed up again. It could be that the United States has experienced all the ills accompanying a recession, without the gains on inflation hoped for by the president.

As his chief economic adviser told an audience of lawyers last week, U.S. experience in the last 10 to 12 years has shown that once inflation is pushed up to a new higher rate, it tends to remain there once the first inflationary shock has passed.

The U.S. inflation rate first accelerated significantly after the Vietnam war. After running at about 1 percent a year during the previous decade, inflation speeded up to nearer 4 percent at the end of the 1960s.

Two huge oil price rises have bumped up the inflation rate since then. The first one pushed the underlying rate up by about 3 or 4 percentage points, to reach 7 to 8 percent in 1974. Measured inflation was higher than this for a while as the first effects of the oil price rise fed through and then disappeared.

Last year's second oil price leap had a swift effect on U.S. inflation. It accounted for much of the first quarter acceleration in price rises this year. The administration's aim was to make sure that this rise did not spill over into increases in other costs. So far wage rates have not risen to offset the effect of higher oil and gas prices. But they have not been depressed by recession either.

And while the administration would like to reduce inflation, it also recognizes the need to bring U.S. oil and gas prices more in line with their world prices. The president's phased decontrol program is now about half way through. There will be upward pressure on prices from this in the year to come, even if crude oil prices remain stable or fall.

Recent government figures on producer prices suggest that faster price rises for consumer products are also in the pipeline. The Consumer Price Index itself remained level last month for the first time in thirteen years. But that owed more to a technicality than to an underlying slowdown in inflation: the treatment of changes in the mortgage interest rate in the CPI both delays and exaggerates their effect.

This could work against the administration again all too soon. Soaring interest rates were an important factor in pushing up inflation earlier this year, as well as being a reflection of high inflation and high inflationary expectations. The big banks which have put up their prime rates in the last two weeks have been careful to say that their move does not mean that rates are bound to rise steadily from now on. Loan demand remains fairly weak, unsurprisingly at this stage of the recession.

But the Federal Reserve Board has made fairly clear its view that interest rates are likely to stay high and, if they move, to go up if it is to meet its money supply targets while inflation stays so high and the economy recovers. Administration officials have also admitted that they expect rates to climb next year. To the extent that the general rise in the cost of money drags mortgage interest rates up, too, this will add directly to inflation.

Carter's proposals are carefully designed to avoid adding too much to the Federal budget deficit next year. His statement includes several references to the need for "responsibility" which in this context usually means restraint.