Consumers expanded their installment debt by $1.4 billion in May, continuing a trend of successively greater monthly increases in outstanding credit that began in March, the government reported yesterday.

A top Reagan administration economist said the increase indicated a strengthening in consumer confidence. However, the bulk of the May increase came in auto loans, which will be much more depressed for June, analysts cautioned yesterday. The swing in auto credit could have caused a drop in net installment credit in June, they said. Auto sales fell sharply last month, disappointing some analysts' hopes of an imminent recovery in that market.

Of the $1.4 billion net increase in debt in May, $959 million came from additional auto loans, according to yesterday's report from the Federal Reserve Board. "We can be fairly sure that it consumer credit didn't repeat that performance in June," Alan Greenspan of Townsend Greenspan commented yesterday. "Autos were extremely poor in June," he said, adding that other retail trade, which affects charge account credit, was also poor last month.

Reagan administration officials have predicted that the economy will begin to recover this summer, led by rising consumer spending. The Commerce Department's undersecretary-designate for economic affairs, Robert Dederick, said yesterday's credit report "suggests that consumer confidence has improved." As this continues, "Greater willingness to assume new debt should augment consumer spending and bolster the prospective economic recovery," he went on.

However, many economists fear that the recovery will be anemic and weak because of continued high interest rates. These could discourage consumer spending on durables such as autos, which are largely financed through debt. The June collapse in car sales followed the ending of a special financing program by General Motors Corp. that had enabled people to borrow for auto loans at below-market rates.

There has been a slight easing in rates this week, with a drop in the Treasury bill rate on three- and six-month bills in the weekly auction this Tuesday.

Continental Illinois of Chicago followed this yesterday with a cut in its broker loan rate to 15 1/2 percent from 16 percent yesterday. Changes in this rate--charged by banks to brokers on overnight loans backed by securities--often are followed by changes in the prime rate. However, Wall Street participants fear that a bulge in the money supply early this month, together with the prospect of huge Treasury borrowings in the rest of this year, may keep rates high.

The May credit report showed a 1.8 percent increase in total credit extensions, Dederick said. This was the fifth consecutive monthly increase in extensions. "While ratios of credit extensions to income and to spending have advanced appreciably since the turn of the year, they remain low by past standards," Dederick said.

The ratio of repayments to personal income is also low, although it was up to 15.6 percent in May from a low of 15 percent in March. "This suggests that installment debt payments are not burdensome and should not pose an obstacle to new borrowing," Dederick said.

Other official figures released yesterday showed a sharp drop in the number of initial claims for unemployment insurance in the week ending June 26. The fall from 550,000 in the previous week to a seasonally adjusted 522,000 indicates "a softening of layoffs" rather than a pickup in rehiring, Greenspan said.

The decline in claims added to the evidence that the recession is slowing or ending, but there is still no strong sign of recovery in the economy, Greenspan said. The evidence is that the economy is "getting into the exhaustion phase of the recession," he said, adding that there will have to be a pickup in new orders before the economy really starts to recover.

Many analysts expect a continued decline in industrial output through last month to be reported.