The degree of success or failure of the Williamsburg economic summit will emerge in the weeks and months ahead. It will depend on how the leaders of the seven industrialized democracies follow up on their pledge to seek greater ''convergence'' of economic policies and how they put into practice the principles on which they all agreed: the need to lower trade barriers, to keep inflation under control, and to reduce interest rates and budget deficits. Reaffirmation of these broad principles may not be an achievement to shout about. But the fact that the leaders avoided confrontation and want to be seen committed to cooperation for the mutual economic good is something on which to build.
Economic summits are not primarily designed to solve problems. They are designed to heighten mutual understanding so that national leaders can proceed to work away at the solutions in a spirit of interdependence and personal knowledge of each other's problems. In this sense every summit is a success.
Of course the political dimension of the summit meeting weighed as heavily as the economic one, if not more so. The final declaration was carefully crafted to paper over differences and enable each leader to capitalize at home on the achievement of some political objective. President Reagan bolstered his image as a world leader, both through skillful moderation of the meetings and by winning for the first time an endorsement of a security statement - a common arms negotiation stance toward the Soviet Union. Japan managed to defuse the sharp criticism of its trade policies. France won a guarded agreement to consider its idea of an international conference on monetary stabilization. Prime Minister Thatcher, for her part, benefits domestically from the statement on national security and the conservative thrust of the pledge to limit government spending. No nation got all it wanted - Mr. Reagan, for instance, did not obtain assent to his optimistic economic views - but most returned home with something politically useful in their pockets.
However, the basic accord and harmony of the summit cannot obscure the lingering disagreements on how to spur the world economy and the challenges to overcoming these disagreements. The onus on the United States is especially great. If the leaders promised to lower budget deficits through ''limiting the growth of expenditures,'' it is plain that the US is the chief culprit in violating this standard. Federal deficits have reached the historical high of $ 200 billion annually and may approach the $300 billion level if not soon brought under control. Yet the Reagan administration is not giving high priority to reducing these soaring deficits, inasmuch as it rejects increased taxes, resists slowing the rate of military spending, and even denies that there is any link between deficits and high interest rates - a position with which American and European economists disagree. The US Congress is thus having to carry the ball on restraining the budget explosion.
It may also be said that the summiteers failed to address concretely what many regard as the most dangerous near-term problem and that is the debt burden of the developing countries. No commitment was made to strength IDA, the soft-loan arm of the World Bank, or provide for some other source of increased aid to help finance this debt. Yet the fact is that sustained world economic growth is closely linked to the state of economic health of the third-world countries. One American trade expert notes that demand from the developing nations has been the major source of export growth for the industrialized world in the past three years. If the industrialized nations cannot export more to the third world, how can they generate a momentum of recovery? It is thus vital to keep the debt-ridden countries on an even keel.
Will the seven nations pursue these problems with renewed vigor - even if this means making some politically uncomfortable choices? The world awaits an answer to that question