Boston — The nation could know by next week whether the recession is over.
Economists are already debating the question. Statistics coming out of Washington in the next several days should provide a strong clue as to whether the economy has at last turned around or must wait another month or longer to do so.
Today (June 10) the Commerce Department is scheduled to release figures on ''advance retail sales.'' These will indicate whether people loosened up their pocketbooks in May. On Friday, April figures on inventories and sales for manufacturing and trade will come out. If inventories have dropped sharply, that could be good news. It would indicate a better chance for a buildup in inventory if May.
Then on Monday, another 10 days of auto sales will be announced. That, notes Alan Murray, a Citibank economist, could show whether the end of General Motors' special financing deal May 31 resulted in a drop-off of sales. Auto sales were up sharply in May. Sales of domestically produced cars ran at a 6.3 million-unit seasonally adjusted annual rate, compared with the 5.5 million-unit rate in April. Sales of imports also picked up, so that total car sales again topped an 8 million-unit annual rate.
The best indicator as to the status of the business cycle will be the industrial production index for May, to be released Tuesday by the Federal Reserve Board. If it is up, it will be ''a good sign'' that the recession is over, Mr. Murray says. Looking at weekly reports on the output of steel, autos, paper, paperboard, coal, and petroleum, Citibank suspects there will be a small rise. Townsend-Greenspan & Co., a New York economic consulting firm, reckons on a small decline.
The administration apparently believes the recovery has not started. President Reagan has declared, however, that it is ''imminent.'' Many economists believe such a declaration is premature, that recovery will only come this summer after the 10 percent income tax cut takes effect.
Citibank, though, sees ''a good case that a consumer-led upturn in the general economy began in May.''
Some encouraging signs besides the upturn in auto sales include:
* Chain store sales were up. The New York bank expects today's figures to show a ''marked increase'' in total retail sales.
* May employment figures were ''encouraging.'' May was the first month since last September when the size of factory payrolls did not contract substantially, apart from the weather-distorted month of February. Also, the average workweek increased slightly.
On the negative side, there was:
* A decline in sales in April. The value of construction put in place in both April and March was also down.
* Factory orders dropped in April, and, Citibank notes, this can have ''a strong bearing on the future course of business activity.''
* The National Association of Purchasing Agents reported that production, incoming new orders, and employment fell shArply in May, compared with April. It was, in fact, the worst performance for new orders and production since December , the association said.
* Business investment is likely to decline. Indeed, Otto Eckstein, head of Data Resources Inc., a Lexington, Mass., economic consulting firm, says the near-term outlook in this area is "very negative.''
So, given such mixed statistics, economists are hesitant to stick their necks out and predict firmly that the recovery has arrived. Leonard H. Lempert, director of Statistical Indicator Associates, for instance, says there are 51/2 chances in 10 that the recession has ended or is ending.
Mr. Murray notes that economists are also cautious because of ''experience with the way data revisions, late-breaking news, and unexpected policy or other shocks can upset a preliminary judgment.'' Moreover, he says, a single month of advance doesn't make a recovery.
He makes a few more points about the recovery.
First, if it's here, it will have come in the face of high interest rates. Many have felt this would be impossible. ''We continue to believe that a recovery is in the cards even if rates don't fall anymore,'' he said. ''But we also continue to think rates will trend down. . . .''
Second, the recovery will not be robust. Since 1950, the average gain in real national output in the first year of an economic upturn has been 7 percent. Mr. Murray expects the first year of this recovery to show only half or slightly more in real gain. That's because the Federal Reserve System has not launched a vigorous expansionary monetary policy.
Third, most businessmen and consumers will not notice much change in the economic outlook for months to come. In fact, economic gloom may deepen as high unemployment and numerous bankruptcies continue for months to come. But the underlying picture is turning brighter.