A modest improvement in the international economic climate this year and next is now expected by most government and private economists, in large part because the United States--still the most influential single economy in the world--has finally pulled out of its deep recession, and is almost certain to have a fairly vigorous recovery, at least through 1984.

According to statisticians at the International Monetary Fund, real economic growth in the industrial world this year and next might be on the order of 3 percent annually, as against a fractional decline in 1982 and increases of barely over 1 percent in 1980 and 1981.

Roughly the same assessment comes from the Organization for Economic Cooperation and Development in Paris, which cites a "fledgling recovery."

Europe will not do so well as the United States, in the OECD view, with growth in just the 1 to 2 percent range predicted, and France and Italy have special problems.

Moreover, while unemployment in the United States has come down from its peak of late 1982, the OECD says that the jobless total in Europe will continue to grow this year, possibly to 20 million, or almost l2 percent of the labor force, by the end of 1984.

Meanwhile, the special and enormous burdens of Third World debtor countries--while alleviated by lower inflation, interest rates, and oil prices--stand as an impediment not only to their own internal recoveries, but to a solid and sustained global recovery.

"In this fragile economic environment, it is hardly surprising that our leading trading partners continue to criticize our domestic policy mix and our international policy stance," economist Michael E. Levy of The Conference Board said in a recent report on the world outlook. They are convinced that American administrations, particularly this one, care little about the impact of their domestic policies on the world economy.

But America's own national interests, as Professor Arthur Schlesinger points out in the fall issue of Foreign Affairs, "must set limits on (the Reagan administration's) messianic passions." Thus, while "ideology calls for chastisement of the debtor nations in the Third World," self-interest forced the Reagan administration to fight hard for an additional $8.4 billion for the IMF.

A growing problem is the intensification of protectionist sentiment in the United States, Europe, and Japan, a response to the prolonged and debilitating recession of 1981 and 1982. Despite the highly publicized commitment to liberal trading principles by world leaders at summits such as the May conference at Williamsburg, Va., major governments have made "voluntary" bilateral deals to avoid what they say would be even worse protectionist measures.

A classic example is the "voluntary" Japanese quota on sales of cars to the United States, which is expected to be renewed next March for a fourth year, to avert a more obnoxious "local content" bill that would require significant percentages of American-made parts and labor to be incorporated into Japanese cars.

In addition, on July 5--only weeks after the May Williamsburg summit--President Reagan imposed tariffs and global quotas for four years on a wide range of stainless steel products, outraging producers in Europe, Japan, Brazil and many other countries.

A supreme irony was the effect on Brazil, depriving it of export earnings at the same time the IMF and the United States and other countries were trying to arrange emergency loans that would avert a possible default with chilling global effects.

At the Williamsburg summit, other world leaders also urged President Reagan to reduce American budget deficits so that "real" interest rates--money interest rates minus inflation--would come down, helping to stimulate economic recovery abroad and ease the enormous debt burden of the Third World debtor countries.

But the prospect is that the budget deficits, running around the $200 billion annual level, are too "hot" a political issue to be touched by either party prior to the presidential election in November 1984. The reaction of financial markets has been to establish "premiums" on long-term interest rates.

And according to most analysts, long-term rates will stay high until some combination of budget-cutting and tax increases significantly lowers the deficits.

The United States is not the only major nation with a fiscal problem. Japan, West Germany and the United Kingdom are also trying to reduce their deficits. Tighter fiscal policies to combat still intense inflationary pressures are also being applied in socialist France, Canada, Italy, and many of the less-developed countries.

Dimitri N. Balatos, vice president and economic adviser to the international division of Manufacturers Hanover Trust Co., makes the argument that another major inhibition to a smart recovery is the volatile nature of exchange rates, which cause trade friction and encourage protectionism.

Balatos predicts that business investment in new plant and equipment throughout the world will continue to be "anemic" as corporations use their improved cash flow, instead, to improve their balance sheets.

" Thus the level of unemployment will remain high, diluting gains in consumer purchasing power, and the volume of international trade will expand a modest 1 to 2 percent in 1983, and 2 to 3 percent in 1984--one half the average rate of growth during the 1974-1980 period," he says.

Perhaps the single most beneficial thing that's happened to the world economy in the past year was the sharp decline in oil prices, even though some analysts last year couldn't decide whether a break in oil was good or bad on balance, despite clear evidence that it was the one-two punch of the 1973 and 1979 "shocks" of major oil boosts that had triggered a new recession.

But the decline in oil prices is singled out even by the cautious bureaucrats at the IMF and World Bank as a major reason for the most prospective improvement in global confidence. Lower oil prices are a major reason for sharply reduced inflation in the United States. Worldwide, lower oil prices are the equivalent of a lower tax on industry and consumers.

Most experts conclude that the unwinding of oil prices has run its course, and even Middle East propagandists are not predicting a resurgence in the near future.

A major beneficiary of lower oil prices are the the hard-pressed oil-importing countries. From a peak of $108 billion in 1981, this group's aggregate current account deficit dropped to $87 billion in 1982, and, according to the IMF, the deficit this year will drop another $19 billion to $68 billion.

On the other hand, even these reduced deficits will be difficult to finance as government aid funds dry up and commercial banks, once excessively anxious to shovel out loans, turn super-cautious.

William R. Cline, a senior fellow of the Institute for International Economics here, estimated in a report published last week that the poor-country current account deficit will continue to run around $75 billion through 1986.

Although this level may be 25 percent under the 1981 peak, Cline thinks it will be exceedingly difficult to finance such debts unless real economic growth in the First World runs at least 2.5 to 3 percent, providing markets that enable the debtor countries to earn enough to service the debts.

But even that won't do it. Cline says, in addition, the richer nations must "also avoid any significant new increases in interest rates and protectionist trade barriers."

His study showed that Mexico and Argentina are "showing major progress," and concludes that while the debt crisis should remain manageable, "it nonetheless seems likely to continue to threaten the world economy and international financial stability for at least the next few years."

Others are less sanguine than Cline: Lord Harold Lever; New York banker Felix Rohatyn; politicians such as Sen. Bill Bradley (D-N.J.) and Rep. Charles E. Schumer (D-N.Y.); and many academic experts such as Princeton's Peter B. Kenen are more pessimistic about "manageability," and think that one form or other of major restructuring of the Third World debt is necessary.

In a recent paper written for the Group of Thirty, Kenen said:

"We may muddle through the next few years if debts can be rescheduled, country by country, and year by year." But this can happen only if the economic export trade outlook for the LDCs turns out to be better than anyone forecasts, and if the LDCs follow even more drastic austerity measures than contemplated.

Kenen doesn't expect these things to happen, and adds:

"On the most sober assessment of benefits and costs, debt repudiation may make more sense than the deflation necessary to muddle through. If we do not muddle through, there will be a rash of crises in the international financial system, and no one knows exactly how to handle them."

Kenen proposes a new institution sponsored by the rich OECD governments that would buy up the loans that commercial banks have made to Third World countries.

The new institution "could charge the banks a price for getting out and might thus deter them from getting in again too fast. For example, it might issue $90 of its own debt for every $100 of debt that it took up. It could then renegotiate the debts of the less-developed countries and give them the permanent relief they require. Having bought debt at a $10 discount, it could cut back interest rates and stretch out maturities at no cost to the taxpayers of OECD countries."

The Cline rebuttal, in which he is joined by much of the financial "establishment," is that the Third World problem is a temporary one of "illiquidity" (a cash flow problem) and not one of insolvency. The critical question (to which no one in authority has yet found an answer) is where illiquidity ends and insolvency begins.