The economy declined last spring, and almost every economic forecaster in the land agreed that a recession had begun. Now, it seems, the Commerce Department will report later this week that things turned around during the summer, with output expanding again in the third quarter.

Understandably, people who have come to think of a recession as a two-quarter decline in real gross national product are going to be confused. Has the nation been in a recession since last spring? Or is it still just something the forecasters say is finally about to happen? The answer appears to be, both.

Given the continuation of 13 percent inflation rates, a further slowdown is the explicit goal of both the Fed and the Carter administration.

The summer rebound carried a speculative frosting that along with a host of international pressures forced the Fed's hand. The price of gold, copper and other commodities shot up even when -- as in the case of copper -- nothing had happened in terms of supply and demand to justify the surge.

But so far as real output is concerned, the gains probably were not strong enough to set the recession clock back to zero. After adjustment for inflation, real GNP fell at an annual rate of 2.3 percent in the second quarter. Chances are the increase in the third quarter will not be that large. If that's true, then the peak of business activity was back in the first quarter -- at least as measured by GNP.

By a consensus of economists, the National Bureau of Economic Research of Cambridge, Mass., long the major center for study of business cycles in the United States, has the responsibility of deciding when to stick on a recession label. The recession call rests on far more than a drop in GNP.

No one at the NBER ever defined a recession as a two-quarter decline in real GNP. That short-hand definition sprung from the NBER never having called a recession that did not include at least a two-quarter GNP drop. This distinction as highlighted because a one-quarter decline in 1966 was not considered a recession. (Revisions in the GNP figures a decade later even wiped out that one negative quarter.)

On the other hand, nothing in the annals of business cycles say that there cannot be a positive quarter after a recession begins. During the 1969-70 recession, for instance, GNP fell for two quarters, rose for two quarters and dropped again for one-quarter before it was all over.

All of this may seem arcane, and in one sense it is. But "recession" is a four-letter word in the political lexicon. And when a slowdown becomes severe enough to carry the label, policymakers feel an added pressure to act.

Back in 1970, economists in the Nixon administration argued strenuously that the country was not in a recession. Even though both fiscal and monetary policy had been deliberately put to work restraining the economy in order to hold down inflation, no one wanted to be thought resonsible for causing a recession. There was a feeling within the administration that some economists were too anxious to make Nixon and his advisers look bad.

After nearly nine more years of economic troubles, the word is little less explosive politically, especially when inflation is running at double-digit rates. There is still some fear among current policymakers, however, that there will be more pressure to stimulate the economy with tax cuts and easier money once there is no doubt a recession is in progress.

That's another reason why the emphasis on whether real GNP turns down -- perhaps by only a tiny margin -- is misplaced. The economy is little different if real GNP is rising, at, say, a 0.3 percent rate rather than if it is declining at the same rate.

The NBER, therefore, looks at a number of economic indicators in calling a recession. Last summer, at the first NBER meeting to discuss whether the economy is in a recession, the economists involved simply said it was too early to tell. The evidence was not conclusive, they said.

To qualify as a recession, the decline in economic activity must last for some time, be deep and affect a large part of the economy. Among the indicators that the NBER watches in addition to GNP are the unemployment rate, industrial production and a so-called diffusion index of how many industries show declining employement.

There has never been a recession that did not last at least 8 months and include a decline in real GNP of at least 1.1 percent, a decline in industrial production of at least 7 percent, an increase in the unemployment rate of at least 2.3 percentage points and declining employment in at leat 71 percent of major non-farm industries.

So far, none of these test has been met in 1979.

Third-quarter real GNP will be close to its first-quarter level. Industrial production in Septembr will probably be less than one percent below its peak in March. At 5.8 percent, the unemployment rate in the third quarter was only 0.2 percentage point above the low of the second quarter. And over the last six months, 50 percent of industries still were increasing employment. In September, 55 percent did so.

At this point, most forecasters are predicting enough of a drop in economic activity to meet all these tests, thought some of them perhaps will just barely make it. Here's why:

Consumer incomes generally have not kept pace with inflation, even when using a more realistic measure of inflation than the consumer price index, with its overly large component for mortgage interest costs. Eventually, even in an inflation-plagued economy with a buy-it-now-before-the -price-goes-up syndrome, this drop in real buying power will mean less spending.

Moreover, after last week's big jumps, interest rates are now so high that banks and others making installment loans will be tightening their credit standards. Poorer credit risks may be shut out.

Even higher mortgage interest rates and lenders beginning to feel a money pinch are making it harder and harder for people to refinance their homes or move up to larger ones while taking a portion of their equity out as cash. With that source of funds drying up, and with personal savings rates already at an abnormally low 5 percent or so, weaker consumer buying ought to contribute to the recession from here on.

The same mortgage situation also will begin to squeeze construction of new homes. Housing construction loan rates are hitting 15 percent, and mortgage rates were close to 13 percent as of last week. And if that is not discouraging enough, the flow of new money into savings and loan associations dried up altogether in September.

Thus housing experts expect the rate of new housing starts to trumble from 1.8 million units in August to no more than a 1.5 million rate by early 1980. If the Fed keeps interest rates high for very long, a housing recovery will be delayed until the latter part of next year, too, say these analysts.

Business investment, which is still going strong, also will be hurt by higher interest rates. Spending for new plants and equipment, which probably will have risen about 5 percent in real terms this year, should be down by several percentage points in 1980. The negative signs are already evident in the flow of new orders for non-defense capital goods.

Meanwhile, the higher cost of borrowing money is making it more and more expensive for businesses to finance their inventories. With sales already none too strong, a significant drop in the rate of accumulation of inventories was in the cards. In fact, Federal Reserve Chairman Paul Volcker said speculative inventory building is a disturbing development that the Fed's tighter policy is supposed to correct.

One key to just how severe the recession is in 1980 will be whether businesses actually start to liquidate inventories or just slash the rate at which they are being accumulated.

Federal government purchases of goods and services should be rising next year, perhaps by about 3 percent in real terms. But state and local government spending is likely to rise hardly at all after adjustment for inflation.

The nation's trade balance will be a source of strength, however, as exports increase more rapidly than imports next year.

All this adds up to a recession, probably lasting until spring. It will reduce inflation, but perhaps only down to the 9 percent range. Still, without the recession, Carter administration economists fear that wage increases, which have been considerably less than inflation over the last year, will accelerate and keep inflation high.

Perhaps all the forecasters will be surprised again. Maybe the economy will keep chugging along with only a tiny setback here and there. Maybe the tests of a recession will not be met.

But keep this in mind: The federal budget is moving from stimulating the economy to restraining it, a swing that will be worth about$50 billion by late next year; and the Federal Reserve is tightening, too.

A recession is still the odds-on-favorite.