The Federal Reserve Board raised interest rates again Tuesday in its attempt to cool the economy and head off inflation. Banks quickly responded by increasing their prime lending rates.

The Fed lifted the discount rate on loans to its member banks to 4%, from 3.5%, and hiked its target rate on overnight loans of bank reserves, better known as the federal funds rate, to 4.75% from 4.25%.

Within an hour, New York's Chase Manhattan Corp. led the banking industry response by raising its prime lending rate to 7.75%, from 7.25%, matching the central bank's half-point rate increase.

Not far behind in taking the same action were Norwest Corp., Citicorp, Chemical Banking Corp., and several other major banking companies.

The bond market rallied on the news, particularly prices of the longer maturities. Bank stocks also rose, after an initial bout of investor jitters about how banks would react.

It was the fifth time this year that the Fed has raised the funds rate and the second time it has raised the discount rate.

Tuesday's move came in conjunction with the Fed's monthly meeting of its open market committee, which sets monetary policy. In a closely scrutinized statement, the central bank said:

"These measures were taken against the background of evidence of continuing strength in the economic expansion and high levels of resource utilization. The actions are intended to keep inflationary pressures contained and thereby foster sustainable economic growth.

"The Federal Reserve will continue to monitor economic and financial developments to gauge the appropriate stance of policy, but these actions are expected to be sufficient, at least for a time, to meet the objective of sustained, noninflationary growth."

Most bank stocks posted respectable price gains in the wake of the Fed action. Late in the session, the Standard & Poor's bank index was up 1.07% for the day.

Helping lead the rally were the depressed shares of Bankers Trust New York Corp. and J.P. Morgan & Co., which have staged a minor revival recently.

Investors view the two money-center institutions and their big trading operations as the top beneficiaries of the Fed's latest move.

"The greatest benefits of a rate hike go to them," analyst George M. Salem of Prudential Securities said Tuesday.

Bankers Trust was up 62.5 cents a share, to $70.625. It is up 5% in value in the past week, but is still 17% below its high this year, reached last Feb. 2.

Morgan was up 37.5 cents, to $64.875 a share, and has gained nearly 4% over the past week, but still has ground to make up. It is 10% below its high, also set in February.

Meanwhile, Citicorp advanced $1.25 a share, to $43.75, partly on a reiterated "buy" rating from Mr. Salem; Chemical was up 75 cents to $39.125; and Norwest was up 62.5 cents to $26.875.

There was little criticism of the Fed action by economists, most of whom had anticipated a rate increase.

"This is an appropriate tightening, a normal occurrence in a mature expansion," said Eugene J. Sherman of M.A. Schapiro & Co. Inc., New York.

He said he now expects the central bank to "step aside for three months to assess the impact of its latest tightening" and then probably raise rates again at the Nov. 15 meeting of the open market committee.

Mr. Sherman said he felt the Fed would have room to tighten further by then because economic growth is likely to "continue to out-pace productive capacity, with the result that inflationary pressures will continue to intensify."

He said he felt the new federal funds target level of 4.75% puts monetary policy "at the midpoint of neutrality."

Earlier this year, Fed Chairman Alan Greenspan said the central bank was striving for a neutral rate policy that was neither expansionary nor too tight.

He did not, however, define what he meant by neutrality.

Mr. Sherman said his definition of neutrality is based on a six-month average of the core consumer price index annualized, plus 1.5%, within a range of plus or minus 50 basis points.

"Core CPI is 3.2% through July," he pointed out. "If you add 1.5%, you get 4.75%, so we are right at the midpoint, using my criteria." As he sees it, this also means the Fed could tighten yet another 50 basis points "and still be in the neutral zone."

Mr. Sherman said he believes the Fed has still not caught up with the strength of the economy with its tightening moves and, at its current pace, will not be in a restrictive monetary policy mode "until into 1995."

But some economists are skeptical. "By acting in anticipation of inflation, the Fed is risking the economic expansion," according to David Levy of Bard College in Annandale, N.Y.

In a recent study, the economist said productivity gains and other factors ensure there is "no danger of a lasting acceleration of inflation, even if the economy does well over the next 12 months."

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