Yesterday the U.S. dollar was worth 18 percent more against the mark and 21 percent more against the yen than when President Reagan took office. On average, the dollar's value is now about 23 percent higher against the currencies of major U.S. trading partners than in January 1981.

This tremendous change has occurred with little comment in Washington. But it is having a big effect on the economy.

Some analysts think today's high exchange rate is a major factor in the current recession. It is one of the reasons why many forecasters predict a slow and anemic recovery. And, on the brighter side, it has contributed to the dramatic slowdown in inflation in recent months.

Despite the impact that the dollar has on the U.S. economy, the administration does not have an explicit exchange rate policy. Since taking office, Reagan officials have disclaimed responsibility for the dollar's performance in foreign exchange markets. Currency values should be fixed by the markets without official interference, they have said so far.

President Reagan's economic program, however, has a crucial influence on the dollar. Just as Margaret Thatcher's policy in Great Britain of fighting inflation with tight money led to a sharp rise in the value of the pound, so the tight money policy Reagan supports has helped to push up the dollar.

High U.S. interest rates--the result of this tight money, particularly when combined with prospective large federal deficits--have made the dollar increasingly attractive to overseas investors. They can earn much more by putting their money into dollars than into marks or yen.

Not all of the dollar's rise in the last two years or so can be explained adequately by economists, but interest rate differentials between countries are "the basic reason" for the dollar's rise, says former assistant Treasury secretary C. Fred Bergsten.

When the dollar climbs, it makes U.S. goods harder to sell overseas--because they cost more in terms of foreign currency--and foreign goods cheaper to U.S. consumers. This phenomenon tends to weaken U.S. economic growth. Firms in the United States face stiffer competition from foreigners both at home and abroad and so are unable to sell as much as they would if the dollar were cheaper.

In time, the drag on exports from a higher dollar, combined with the boost to imports, will worsen the U.S. trade balance.

This is being helped now by plunging oil imports, by the initial effects of the dollar's strength--which make it possible for Americans to buy the same amount of goods from overseas for fewer dollars--and by the recession, which reduces demand for foreign goods in the same way it cuts into consumer purchases from domestic producers.

However, recent official figures suggest that the dollar's rise already has had a substantial impact on trade. The latest Commerce Department release on the gross national product shows that exports in the first quarter of 1982, when measured at a seasonally adjusted annual rate, were 6 1/2 percent lower in real terms than a year earlier. Imports were 2 percent higher despite the recession.

Overall, the worsening net trade balance accounted for $12.7 billion of the $34.2 billion decline in total gross national product--measured in constant 1972 dollars--between the first three months of 1981 and the same period this year.

As the economy recovers, the high dollar likely will encourage imports further. Consumers, who are expected to lead the way out of recession after the July 1 tax cut, will spend more of their money on foreign goods than if the dollar were lower. This will weaken the recovery in U.S. production.

There are those who believe that the costs to output and employment from a high exchange rate are more than outweighed by the benefits in terms of lower inflation. After all, economic policymakers are fighting inflation with tight money and slow growth. A high exchange rate is just one of the channels through which this policy operates.

A strong dollar cuts the cost of imports, holding down these prices directly, and indirectly may force U.S. firms to curb price rises to stay competitive. In addition, some analysts believe that the dollar's recent strength has encouraged oil producers to hold down prices, as these are fixed in dollars. When the dollar is strong, oil exporters benefit.

Allen Sinai of Data Resources Inc. estimates that "anywhere from 1 to 3 percentage points of a 10 percent or so improvement in inflation" over the last 18 months has been due to the strong dollar.

But what if interest rates fall--as everyone hopes they will--and the dollar weakens--as many believe it should? In that case, the inflation improvement from the strong dollar likely will be reversed as import prices rise. In the meantime, the economy would have suffered some additional loss of jobs and output because of the high value of the dollar over recent months, but for no permanent gain on inflation.