Federal Reserve Chairman Paul A. Volcker, appointed yesterday by President Reagan to a new term, came to office nearly four years ago with a conviction that the nation's economic future was threatened by high and rising inflation, and that the Fed must help stop it.

In pursuit of that goal, Volcker led the central bank to adopt policies that curbed inflation, but at the cost of the highest unemployment rates in 40 years and record numbers of business bankruptcies. The high interest rates generated by those policies spilled over into international financial markets and helped produce recessions abroad in both industrial and developing countries.

Remarkably, respect for Volcker mounted with the costs of the anti-inflation policy. His conviction about the dangers of inflation was shared by the Reagan administration and, it turned out, to a large degree by the American public.

No hue and cry ever mounted in Congress for his ouster, and when Reagan administration officials began seeking advice about whether Volcker should be reappointed, numerous members, including Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), gave the Fed chairman their full backing.

The Fed's policies under Volcker have had their critics. Liberal politicians and economists, and monetarists as well, blamed the Fed for economic overkill. At various times, Reagan and other administration officials, including Treasury Secretary Donald T. Regan and Undersecretary for Monetary Affairs Beryl Sprinkel, pointedly complained about aspects of policy. The money supply, they said, was growing too fast or too slowly.

Had the Fed implemented its policies more carefully, the administration criticism ran, the deep recession that ended in December might have been avoided or much less severe.

But with Reagan's decision to reappoint Volcker, the administration has implicitly embraced the implementation and results of the Fed policies, not just the overall anti-inflation goal. In effect, Reagan has given up an opportunity during the presidential campaign next year to blame the Fed for the recession while taking credit for the drop in inflation and the current economic recovery.

Why did the president reappoint Volcker? It was partly because of Volcker's stature and partly because there was no obvious replacement who was regarded as a Reagan partisan. In addition, there apparently is no disagreement between Reagan and Volcker over the goals of monetary policy for coming years.

Volcker has come to be so highly regarded by many influential participants in financial markets here and abroad, and by officials in other countries, that there were warnings that replacing him could add to uncertainties in the markets and boost interest rates. Moreover, the warnings ran, dumping Volcker could upset some of the delicate negotiations over how to prevent international loan defaults by nations such as Mexico and Brazil.

President Carter named Volcker to replace G. William Miller--who became secretary of the treasury--in part because he needed a man with impeccable credentials who could calm jittery financial markets. In a sense, Reagan found himself in a similar situation.

Today, the U.S. dollar is as strong as it was weak in 1979. But the debt situation in some developing nations is potentially a greater problem than a weak dollar. Domestically, interest rates are unusually high relative to inflation, and many economists say they believe that any sustained increase in them could abort the recovery in 1984.

But the other major economic problem of 1979, inflation, has been reduced substantially.

Volcker, a pragmatic economist and astute politician, has helped restore the Federal Reserve's credibility as an institution devoted to keeping inflation in check. Although the 19-member Federal Open Market Committee sets policy for the Fed, Volcker has been an effective leader in that collegial group, achieving a policy consensus with few dissents.

The Fed chairman also has proved an effective advocate for the bank's policies, whether in dealing with financial market participants or testifying before Congress.

But his crowning policy achievement has to be his embrace of a monetarist approach in October, 1979, only two months after he moved from the presidency of the New York Federal Reserve Bank to become Fed chairman.

The Fed had been setting targets for growth of the money supply for several years. Operationally, it tried to hit the target by manipulating certain short-term interest rates. Whenever rates rose, the Fed took a lot of political heat.

Volcker and the FOMC changed that by focusing instead on the provision of reserves to banks. Banks must set aside a portion of their deposits in reserves. When the money supply grows, more reserves generally are required. If the Fed does not supply them, interest rates usually rise and money growth slows.

Volcker knew that controlling inflation would require a tight money policy and much higher interest rates. But if the Fed was not directly setting rates, the political flak could be turned aside.

Last year, with the recession still worsening and inflation much lower, Volcker and the FOMC dropped their close, sometimes mechanical pursuit of the money growth targets to seek an economic recovery. The switch in Fed policy and the effects of the long recession helped lower interest rates, set off an explosion in stock prices and, at the end of the year, launched the recovery.

Throughout Volcker's chairmanship, the Fed's job has been made far more difficult by federal budget policies. The Reagan tax cuts, defense spending increases and the drop in inflation have led to very large deficits. Treasury borrowings to finance those deficits are helping to keep interest rates high.

Volcker has advocated more spending cuts, and failing that, higher taxes to reduce the deficits. He is largely at odds with Reagan on the tax side, but then so are some of Reagan's economic advisers.

However, the Fed chairman's economic goals remain similar to those of the president. Volcker wants monetary policy to accommodate an economic recovery that will be strong enough to reduce unemployment but not so strong that it will allow inflation to take off again. Achieving those goals will require a delicate balancing act for monetary policy.