As Western Europe enters its fourth successive year of recession, there are deep anxieties that the shrinking volume of world trade and the impact of austerity plans could prolong the period of stagnation through the end of the decade.

The European economies have found it increasingly difficult to break out of the depressive spiral as two major engines of the region's economy--the United States and West Germany--offer no immediate prospects of vigorous growth.

Most economists trace the recession to urgent efforts undertaken by many Western nations to curtail double-digit inflation ignited by a second series of oil price increases in 1979. Two years later, the clampdown had caused interest rates to soar toward 20 percent.

High interest rates have magnified the debt burdens of many countries, forcing them to cut back drastically on imports. This, in turn, has damaged hopes for the kind of export growth that nurtured much of Europe's prosperity in the postwar era.

At the same time, the overvalued dollar, while creating new opportunities for European exports to U.S. markets, has meant higher prices, in terms of European currencies, for imports of oil and other raw materials.

Unemployment in Western Europe, already at record postwar levels, is expected to surpass 11 percent this year and impose ever greater strains on the extensive social welfare systems in many countries.

In addition, the cumulative effect of low growth and high labor costs has cut profit margins and inhibited major investments in new technologies that will shape future markets. As a result, Europe lags badly behind the United States and Japan in such advanced industries as microelectronics.

These factors led the European Community's Brussels-based Executive Commission, which usually judges the condition of the 10 member states with utmost caution, to conclude in its 1982-83 economic report that "the European economy entered a second downward phase in a double-dip recession" last autumn and that "the risk of a lasting deflationary situation cannot be excluded."

The Organization for Economic Cooperation and Development (OECD), the 24-nation body that coordinates the economic programs of the leading industrialized democracies, reported in its year-end economic outlook that unemployment and growth prospects are worse in Europe than elsewhere in the developed world.

The organization said that the combined gross national product of European countries fell by one percent in the second half of 1982 and, at best, will rise only 1.5 or 2 percent by mid-1984.

Meanwhile, European unemployment is expected to increase by nearly a million people every six months to 19.5 million by mid-1984, and prospects for improvement remain dubious for the ensuing years.

In Europe, as in the United States, one positive element of the protracted recession has been the rapid decline in inflation, which is predicted to range from 3.5 percent in 1983 in West Germany to 16.25 percent in Italy with most countries clustered near 5 percent.

The OECD, however, suggested that the cost of tight money policies, pursued simultaneously by many countries eager to lick inflation, may have been too high in terms of the stubborn recession and record unemployment.

The social benefits provided by many European nations have cushioned the painful shock of widespread joblessness. Indeed, the public reaction to mass unemployment has been remarkably subdued so far, with minimal strikes and few violent demonstrations.

Nonetheless, the rising tide of bankruptcies and the gloomy prognosis about prolonged stagnation has intensified concern that even relatively stable and prosperous countries, such as Denmark and West Germany, may face a new era of political and social disarray.

To thwart that possibility, many European countries are planning to shift the emphasis of their economic programs to solving the unemployment problem. A survey of major European countries, however, shows little hope for a sustained recovery unless there is a dramatic leap in growth elsewhere, especially in the United States.

West Germany: Many economists believe that for Bonn to help pull the rest of Europe out of recession, its economy must expand well beyond the 3 percent level that is thought necessary to increase the number of available jobs. Official estimates predict little or no growth for 1983 after a 1.25 percent decline in 1982.

Like its European neighbors, the West German economy has become tied to obsolete industries, bloated budget deficits and inefficient production due to a low levels of investment.

A recent Commerzbank study showed that 75 percent of West German machinery is out-of-date. Only one firm, Siemens, ranks in the top 15 of the world's high-technology electronics firms.

The West Germans are acutely vulnerable to the global recession, because they derive 29 percent of their gross national product from exports, which have found fewer buyers lately in a world of tight money.

Any major effort to invigorate the economy may have to wait until after the March elections, in which Chancellor Helmut Kohl will seek a strong mandate to undertake reforms that would reduce some social subsidies and lower taxes on corporations in an attempt to revive profits and investment.

France: The Socialist government of President Francois Mitterrand took office in June 1981 committed to a pro-growth policy of demand stimulation. But as its inflation soared while other countries embarked on austerity plans, France was forced to devalue the franc twice and radically alter its economic program to slow the massive loss of central bank reserves.

A 27 percent decline in the franc's value since 1981 actually worsened the French trade balance because more expensive imports outweighed a slight rise in exports. Prior to the end of 1982, External Trade Minister Michel Jobert estimated the year's trade deficit would amount to $14 billion.

Paris is now following a stringent austerity budget, and Mitterrand has abandoned some Socialist orthodoxy to rescue French manufacturers and exporters.

He also has evoked the specter of protectionist measures to rectify France's trade imbalance. In placing restrictions on imported video recorders recently, Mitterrand said he was seeking to encourage "the reconquest of the domestic market."

Britain: Since Prime Minister Margaret Thatcher took office in 1979, unemployment has jumped from 6 to 12 percent. Inflation has improved dramatically, falling to 7.75 percent from a peak of 20 percent just two years ago.

Britain enjoys a strong balance of payments position due to revenues from North Sea oil, but the government is fearful of touching off a new bout of inflation and has sought to soft-pedal expansion. As a result, the British economy is expected to grow no more than 1 percent this year after a decline of 0.5 percent in the last half of 1982.

Italy: More than other European Community countries, Italy still struggled in 1982 to control inflation, which at 17.25 percent was far out of line with the Western European average of 10 percent.

For the first half of the year, the economy grew by 3.6 percent --much better than the rest of the EC.

But the need to impose a tough set of financial measures in mid-year, including a huge increase in taxes, brought down the growth rate markedly in the latter months to an annual average of less than 1 percent.

Depending on how the country's unions respond to pleas to avoid strikes, OECD economists predict a very slight increase in growth this year.

The Netherlands: The new center-right coalition government, like the one in Belgium, took office calling for a campaign of economic austerity and sacrifice. The Dutch government plans to cut public spending by 10 percent this year and has banned, for the time being, automatic cost-of-living increases in labor contracts.

Suffering from many of the same structural problems as West Germany, the Netherlands expects to endure its third consecutive decline of 1.2 percent in gross national product this year.

Sweden: Socialist Premier Olaf Palme returned to power in 1982 with a moderate plan for government spending and warned the country to expect a 4 percent decline in living standards in the next year.

Palme also ordered a 16 percent devaluation of the krona to improve his country's commercial position, a move that irked some of Sweden's major trading partners, who warned that competitive devaluations might rekindle the kind of beggar-thy-neighbor policies that damaged the world economy in the 1930s.

Economists in Washington and Western European capitals emphasize that any recovery will depend on the nature and extent of an upturn in the U.S. economy.

A grave fear in Europe focuses on the likelihood of huge budget deficits igniting another spurt in U.S. interest rates, thereby renewing upward pressure on the dollar.

European Community officials believe that crucial steps on the road to recovery include halting the enormous fluctuations in exchange rates and alleviating some of the massive debt problems facing many developing countries.

U.S. and European governments have started to cooperate more closely on these issues in recent months. They hope that the recent drop in interest rates will continue so that exchange rates can find a stable relationship.

In addition, the United States has finally conceded that the reserves of the International Monetary Fund should be increased from $62 billion to more than $100 billion this year to cope with the burgeoning needs of many nations to find alternative means to service their debts.

But a potent recovery program to pull the world out of the depths of protracted recession may require even more collaboration among Western economies on the timing of new measures to stimulate growth.

John Williamson of the Institute for International Economics in Washington believes that any expansionary moves by the United States may be insufficient and would require the concerted help of other countries that are in a position to prod their economies toward greater growth.

Williamson believes that West Germany, Japan, Britain and Canada should join with the United States to form a nucleus of expanding economies that could break out of the downward cycle that has entrapped most of the Western world.

If such a vanguard could generate enough growth to pull other countries out of the doldrums, the world economy might be able to reverse itself and revive the course of free trade and investor confidence that fueled much of the West's economic momentum after World War II.