Alan Greenspan, as The Economist said the other day, will become ''the most important economic policymaker'' in the world when he takes over from Paul Volcker as chairman of the Federal Reserve Board this summer.

In a way, the reaction to this prospective shift has been surprisingly mild so far. It reflects the generally held view that if Volcker had to go, Greenspan was a good choice to succeed him. But there are two serious reservations about Greenspan.

The first, expressed by a European, is that ''Alan doesn't look to be as independent as did Paul.'' And the second is that Greenspan lacks Volcker's international experience.

To deal with the latter issue first: Obviously, Volcker's eight years of dealing central-banker-to-central-banker can't be duplicated by anyone. And Volcker had on-the-job training in managing the Third World debt crisis.

But Greenspan has broad international experience, and is no stranger to global economic diplomacy. It is sometimes forgotten that as economic adviser to President Ford, he helped shape the economic summit process when it began in 1975 and 1976. And on some technical money-market and banking issues, Greenspan may have a better grounding than Volcker.

It is the other concern that needs to be examined closely. It is that somehow because of Greenspan's Republican political connections and better access to the White House, the Fed's independence may be in jeopardy.

Conservative political analyst Kevin Phillips (who once worked for Greenspan) writes in his newsletter that, ''GOP loyalist Alan Greenspan's selection . . . will escalate the politicization of the 1987-88 economy -- and probably also increase the chance of volatility or even a recession.''

Phillips' concern about ''politicization'' is based on Greenspan's close GOP ties, his debt to Reagan for the job, and the fact that all other Fed governors are Reagan appointees. He assumes the Reagan dominance of the Board helped decide Volcker to get out -- and that Greenspan might be able to control such a board even less than Volcker.

Democratic Sen. William Proxmire, in a similar argument, believes that if inflation becomes a threat in 1988, Greenspan won't be able to persuade the board ''to jam on the monetary brakes.'' House Speaker Jim Wright comes at it from the opposite point of view. He sees Greenspan as ''one of the leaders of the austerity gang'' who will run up interest rates too high.

So Phillips and Proxmire worry that Greenspan will be too weak to control inflation, while Wright thinks he will be too tough in doing so.

Past performance is not always a reliable guide, but 11 years ago, Greenspan, then chairman of Gerald Ford's Council of Economic Advisers, pursued an anti-inflation fiscal policy that some believe cost Ford the election, as the economy turned a recessionary corner.

It seems to me that Phillips -- who thinks solely in political terms -- is overly concerned if he believes that either Greenspan or the other governors would yield their independent judgment of economic issues in order to help the Republicans win in 1988.

It's one thing to assume that Greenspan would prefer to see a Republican rather than a Democrat elected in 1988. It's safe to say he would. But the notion that he would advocate monetary-policy action or inaction to get a Republican elected ignores the man's integrity.

This isn't to say that Greenspan will make all the right decisions, any more than Volcker has or might have if he had stayed on. The difference is that Volcker over the past few years has been almost insulated from criticism because he succeeded in bringing both interest rates and inflation down. That's why financiers all over the world love him.

Greenspan knows that this comfortable situation won't continue -- nor would it have continued under Volcker. Inflation will go up some, and so will interest rates. And when that happens, the heat will be on Greenspan.

My guess, based on talks with him over the years, is that he knows that questions relating to his political independence from the White House will be raised until there is a performance record to show that he takes an oath of office seriously.

It is clear that Greenspan will have more access to the White House than did Volcker, who had none. But whether that will mean Greenspan can influence the administration to be more responsible -- say, in approving some kind of tax increase to shave the deficit -- or that the White House will push Greenspan to be accommodating, only time will tell.

If I have a worry, it more nearly matches Wright's than that of Proxmire or Phillips. Greenspan, a market-deregulator, tilts to the right of Volcker. My guess is that he is so committed to whipping inflation that he would risk recession, if in his mind that were necessary, no matter who is running for election.