The economic news last week tended to confirm that the recession may have hit bottom in May, but developments in financial markets offered new threats to the longevity of the recovery most forecasters expect later this year.

The uncertain outlook has prompted the Reagan administration to launch a far-reaching review of its economic policies that could lead to changes if the high level of interest rates continues and the recovery proves weak, Treasury Secretary Donald T. Regan disclosed.

Several statistics for May, coupled with earlier reports on employment and retail sales, indicated that the recession may have ended 10 months after it began last July. Industrial production declined only 0.2 percent after much larger drops in both March and April. Housing starts jumped above a 1-million unit annual rate for the first time since the recession began. And personal income climbed 0.7 percent, the largest increase since November, and personal outlays increased 1.3 percent.

Commerce Secretary Malcolm Baldrige, ticking off some of these numbers, told reporters he expects the gross national product, adjusted for inflation, to post a small increase for the current quarter following two quarterly declines. His department's so-called flash estimate for the current period will be available this week.

Federal Reserve Chairman Paul A. Volcker told Congress' Joint Economic Committee that the latest statistics are those that "tend to accompany a leveling out of a recession and the beginnings of a recovery."

But not all the signs are pointing even roughly in the same direction. The latest information about the flow of new orders shows them still declining, and the commodity prices that are particularly sensitive to economic conditions are still falling. The worst news, however, was that both short-term and long-term interest rates bounced upward sharply last week.

House and Senate conferees reached agreement on a federal budget resolution for 1983 calling for a deficit of about $104 billion, substantially less than the numbers the financial markets have been kicking around for months. But the markets reacted skeptically and both the stock and bond markets finished the week down significantly. The Dow Jones Industrial Average hit its lowest level in more than two years, wiping out the spring rally that was seen by some people as heralding an economic recovery this summer.

Short-term interest rates shot upward, particularly on Thursday when rates on large 90-day certificates of deposit, a major source of lendable funds for big banks, jumped a full percentage point. From Friday to Friday, the CD-rate went from 13.7 percent to 15 percent. Even before Thursday's remarkable increase in short rates, Citibank, which had been the only major bank with its prime lending rate still at 16 percent, raised it back to 16 1/2 percent.

If the banks' cost of funds does not drop this week, the prime probably will go higher. In fact, Secretary Regan said during an interview at a Washington Post luncheon, "In light of what the markets have been doing in the past two or three weeks, the probabilities of the direction of the next move are up for the prime, unfortunately."

Cross-currents are not unusual when the economy is approaching a turning point. Different indicators can point in several directions at once. But this is the first time interest rates have been so high at the bottom of a recession--if indeed it is the bottom--and certainly they aren't supposed to be going up rapidly.

This potpourri cannot be sorted out with much confidence by economic forecasters precisely because the nation is into uncharted territory as far as interest rate behavior is concerned. Normally, interest rates would not be rising because the recession would have reduced corporations' demand for credit and they would have gotten their balance sheets into much better shape. Instead, the demand for short-term credit has continued to rise because of the severe squeeze on profits, a by-product of the entire process of disinflation.

The key question a forecaster has to answer at this point is whether more than a weak, temporary recovery is possible without a significant decline in interest rates. Each week that passes without such a decline extends the squeeze on businesses and heightens the possibility any recovery will quickly be aborted.

However uncertain the outlook may be, forecasters must forecast. Economists in the Reagan administration, for instance, must shortly come up with a revised version of their predictions since the president is obligated to send one to Congress by the middle of next month. Those engaged in that exercise would not discuss it in detail last week, but one administration source said the new forecast will not be changed significantly from the current official line which has the recovery continuing indefinitely.

In fact, the consensus forecast among most private economists right now is for a moderate recovery that will be set off by stepped up consumer buying in the wake of the 10 percent cut in personal income taxes July 1. The consensus is that the recovery will continue for quite some time, though its pace will be modest enough that unemployment will drop very slowly.

For instance, Wharton Econometric Forecasting Associates expects the economy to grow at about a 4 percent rate for the next six quarters, with inflation running about 6 percent over the period. In the Wharton forecast, the unemployment rate, which was 9.5 percent in May, falls only to 8.6 percent by the fourth quarter of 1983.

But Wharton acknowledges the uncertainty surrounding interest rates and Federal Reserve policy and offers a less likely, alternative forecast labeled "Triple Dip" in which the recovery is aborted by an increase in interest rates late this year. "Triple Dip" refers to the fact that another move in the direction of recession would be the third in three years.

"The two most likely scenarios under which interest rates could rise dramatically later this year are an increase in private-sector credit demands colliding with the financing needs of the federal government, and a sharp reduction in the rate of increase in the money supply following two or three quarters of 'excessive' money growth," Wharton concludes.

A few economists, on the other hand, are flatly predicting the recovery will not make it. Among them are H. Erich Heinemann and Charles Lieberman of Morgan Stanley & Co., the New York investment banking house.

Heinemann and Lieberman expect the economy to grow at about a 3 percent annual rate in the final two quarters of this year and then slow down and begin declining before 1983 is over. Real output in the final three months of 1983 would be lower than in the last quarter of 1982--indeed, it would be a minuscule 0.1 percent higher than it was in the first quarter of 1980.

Ironically, the Morgan Stanley economists believe the recovery will peter out, in part, because they expect consumers to save a significant portion of their tax cuts rather than spend them. If the Federal Reserve sticks to its money growth targets, however, they expect the demand for credit will be greater than can be accommodated even with the added personal savings, and at the same time have interest rates falling.

In their forecast, the federal budget deficit continues to rise as the weak economy holds down revenues and "the increase in personal savings ends up in effect being invested in Treasury securities," they say.

Add Heinemann and Lieberman:

"It is in the investment sectors of the economy that the greatest risks emerge. The combination of high real interest costs, weak corporate liquidity, and indifferent business prospects is likely, in our judgment, to lead to lower levels of outlays for both new plant and equipment in 1982 and 1983.

"As we have argued many times previously, the present overvaluation of the dollar should persist so that the export sector of the economy is at best neutral, and may in fact contribute to additional weakness.

"Business inventories are now in the process of stabilizing--a critical factor in our expectation of a limited improvement in the economy this summer--but are unlikely, in our opinion, to provide meaningful strength next year.

"Federal national defense purchases of goods and services are of course on the upgrade, but this sector is far too small to provide much dynamism for the overall economy."

With such a weak economy, the unemployment rate comes down only to 9.3 percent later this year and is up to 10 percent by the end of 1983. Even with such weakness, Heinemann and Lieberman expect inflation to run between 6 percent and 7 percent next year.

Which forecast is correct? The consensus and its optimistic neighbor from the Reagan administration, or that of Heinemann and Lieberman and Wharton's "Triple Dip" alternative? Obviously, no one can be sure because no one can predict with any certainty what is going to happen to interest rates, or how the Federal Reserve would respond if the recovery ended after only a few months.

Perhaps the most significant feature of almost every forecast these days is that the forecasters believe the risks are far greater that the economy will be weaker than expected, not stronger. Certainly the behavior of interest rates last week reinforced that fear.

As one administration source puts it, "High rates could zap the recovery. They certainly are a threat to the longevity of it. Financial markets are expressing their extreme dissatisfaction with the direction of both fiscal and monetary policy. They are confronting a low of uncertainty, and they are reacting accordingly."