The U.S. economy is gripped by what has become the most debilitating recession in four decades. A recovery has not yet begun. When one does emerge later this year, as still seems likely, there is overwhelming evidence it will be a pale version of the vigorous rebound President Reagan has promised the nation his policies would produce.

This quarter, the gap between the actual level of economic activity and what it would be if the country were at full employment--say, with a 6 percent unemployment rate--is running in the neighborhood of a $360 billion annual rate, according to some estimates. Most of that lost output of goods and services can never be recovered.

Unemployment reached 9.4 percent in April, and administration officials are arguing among themselves whether it will go above 10 percent. The latest weekly figures for unemployment insurance claims indicate the rate is headed higher, and it could take a large jump in June when the usual flood of students looking for summer jobs finds far fewer than usual.

The important issue, however, is neither the depth of the recession nor the precise timing of any recovery. It is, rather, how fast the economy will be able to dig itself out of this deep hole.

Economists in and out of government are steadily revising downward their estimates of the probable strength of a recovery, in large part because of the persistence of high interest rates and the growing financial strains of many businesses. The large individual income tax cut coming July 1 will undoubtedly boost personal consumption spending. Coupled with an end to liquidation of business inventories, that ought to get a recovery going. But other parts of the economy will be adding little to overall demand.

"The trough of this recession ought to have been seen by now," economist Alan Greenspan of Townsend-Greenspan & Co. told his clients last week. "However, there is no evidence to suggest that that is the case." Greenspan, who expects the gross national product, adjusted for inflation, to fall at a 1.7 percent annual rate this quarter, is among those who have lowered their growth forecasts.

"The recovery we project coming out of the current recession is bordering on the anemic. Furthermore, the next eighteen months could turn out to be worse than forecast," Greenspan wrote. Business' financial problems are so severe, he added, that "we do not know whether they might not mean continuing recession."

The level of business investment, which last year's tax cuts were supposed to spur, is shrinking. Small wonder, what with corporate profits on a fast downhill slide, so many existing production facilities idle, and the cost of long-term borrowing still above 14 percent even for corporations with AAA credit ratings. Businesses are so squeezed that about 45 cents of every dollar of cash flow is now being paid out as interest to someone.

The Commerce Department reported last week that after-tax corporate profits dropped in the first quarter to their lowest level, after adjustment for inflation, since 1975. Similarly, the Federal Reserve said manufacturing plants in April were using only 71.1 percent of their capacity, compared with a peak of 88 percent in 1973 and an average of 83 percent between 1955 and 1979. Use of primary processing factories, such as steel mills and copper smelters, fell to 67.7 percent of capacity, breaching the post-war low of 68.2 percent set in 1975.

Housing, also chained down by sky-high mortgage rates, also will do little to add to the recovery. New housing starts dropped 6.4 percent last month to a seasonally adjusted annual rate of 881,000 units, lower than December's level and down 32 percent compared with a year ago.

With the dollar still riding high in foreign exchange markets, U.S. international transactions are also expected to be a drag on any recovery, with imports rising more rapidly than exports.

Depending upon the outcome of the budget struggles between Congress and the administration, increases in federal government purchases of goods and services could well be more than offset by declining outlays at the state and local government levels. In any event, the government sector probably will not be a major source of strength, either.

In the short run, the only reasons to expect a recovery remain the relative strength of consumer spending--retail sales rose 1.4 percent in April--and the likely slowdown in the rate at which businesses are liquidating their inventories. The level of inventories fell at a $39.3 billion annual rate in the first quarter, a rate that is not continuing. At some point, new orders for goods will have to rise just to bring current production more in line with current sales.

But with so little relief from the overwhelming burden of high interest rates on the horizon, businesses will have scant incentive to begin to restock their shelves. They simply can't afford to finance the stocks.

Interest rates, of course, remain the key. Congress is tying itself in knots trying to scale back the size of the federal budget deficit for 1983 and beyond largely in hopes their action might help bring rates down. A string of steadily smaller deficits would certainly mean less pressure on financial markets because the government would be borrowing less. And a meaningful budget agreement could also have a strong psychological effect on financial market participants.

The risk is the near certainty, at least in the short run, that raising taxes and cutting spending to trim the deficits will reduce total demand in the economy by more than would be generated by the drop in interest rates. The benefit would be a more balanced economic situation with some improvement in the hard-hit interest-sensitive sectors, such as housing. In the longer run, less federal borrowing would mean more credit available to finance private investment.

Near-term, however, almost all of the analyses of the impact of reducing the deficits show that economic growth would be weaker, not stronger, unless the brighter budget outlook prompted the Federal Reserve to be more generous in providing money to the economy. Federal Reserve Chairman Paul A. Volcker and other Fed officials have given no hints that they would do so.

To the contrary, Volcker is known to believe that inflation has not been subdued sufficiently to allow much relaxation on the monetary front. Despite the tiny 0.8 percent annual rate of increase in the consumer price index over the last three months, the Fed chairman reportedly thinks wages--nearly three-fourths of the cost of doing business for most U.S. companies--are still rising rapidly enough that the underlying rate of inflation is more like 8 percent than eight-tenths.

The economy is so depressed, however, that real output could probably grow at a 4 percent or so annual rate over the coming 18 months while that underlying rate of inflation continued to come down, Fed officials think. If inflation does continue to subside, they expect such a rate of growth would be consistent with their current targets for money growth.

If growth were substantially weaker than that, or if there were no recovery at all, while money is growing in line with the targets, so their analysis runs, then the targets would have to be raised. Seeking faster money growth would have to be done gingerly to avoid arousing new fears of inflation in financial markets, but it would be justified on the grounds that a given amount of money was financing a significantly lower level of economic activity than intended.

The goal of policy at the Fed is to keep pressure on prices while fostering a recovery, too. Under present circumstances, that simultaneous achievement may be possible. But it also means the Fed has no intention of allowing growth of 7 percent or more that has been common in the early stages of post-war recoveries.

At the moment, restraint is not the problem. It is getting any sort of recovery going. Murray L. Weidenbaum, chairman of the president's Council of Economic Advisers, remains confident that the economy will be expanding in the second half of this year, but he said in an interview, "I don't yet see an abundance of indicators that would enable someone to say the economy has begun to turn up."

The "adjustment process" of working off inventories is well underway and new factory orders had begun to rise, Weidenbaum pointed out. The report on Friday that durable goods orders in April turned down again, he acknowledged, "does not look good, frankly."

How soon, how strong and how long-lasting the recovery is "will be influenced heavily by our ability to get those interest rates down more than we have so far," he continued. There is no new plan under consideration to do that, as was implied by some comments last week by White House officials, he said.

Weidenbaum indicated some impatience with some of the political aides at the White House who make no bones about their feeling that time is fast running out on getting enough of an economic improvement to turn voters back toward the Republicans in the fall elections.

"Politicians always want to know what have you done for me lately," Weidenbaum said. "We will see a continuing improvement in inflation, but the political process seems to have completely discounted that.

"We have been saying since we got there that there is no quick fix. The underlying trend in inflation is 6 percent, half the rate when we got here. That's a fundamental change, and I think it will be a durable change," the CEA chairman declared.

Some other economists, like Volcker at the Fed, would put the number higher, though everyone agrees there has been substantial improvement in inflation. That improvement has come at a very high cost and the payments in 1983 will still be high.

Alan Greenspan, for instance, expects unemployment to still be 8.8 percent in the fourth quarter of 1983, and the gap between actual and potential GNP will still be huge.