The reason is that such manipulation would be a unilateral act that erodes trust in the United States at a time when American debts have reached precarious levels. A reserve currency lasts no longer than foreign confidence in its holder’s ability to pay its bills. In 1985 America owed the rest of the world $104 billion, an amount equal to 2.5 percent of United States gross domestic product, a very manageable burden. Since then, those debts have risen to $9.7 trillion and are approaching 50 percent of G.D.P., a threshold that has often pushed nations into crisis.

Only six countries have held the world’s reserve currency going back to the mid-15th century. All were imperial powers, starting with Portugal, then Spain, the Netherlands, France and Britain, before the United States took over. On average each lasted 94 years in that role. In 1985, the dollar’s run as a reserve currency still looked relatively young, but now it is 99 years old.

China is eager for the renminbi to replace the dollar as a reserve currency, but few investors want to hold a currency governed by strict capital controls. The euro is hobbled by doubts about the European currency union. Even so, America cannot take its reserve currency status for granted, since people are beginning to look for alternative options to the dollar. Witness the recent rise in the price of gold, the speculation in cryptocurrencies and Facebook’s plan to launch its own “global currency.”

This is a fragile and inopportune moment for an American president to sow dollar doubts among the country’s creditors. Mr. Trump has been running up the deficit. Ms. Warren is proposing trillions in spending on new health care, education, child care and environmental initiatives that are likely to have the same effect. And any government that deliberately weakens the dollar will have a harder time finding foreigners willing to invest in United States debt.

Mr. Trump’s constant effort to talk down the value of the dollar is both highly unusual for an American president and oddly timed, since the dollar is one of the few signs of rising United States strength on the global stage.

Though the United States accounts for about a quarter of global economic output, roughly the same share as in 1980, its financial clout has continued to grow by many measures. More and more cross-border loans are issued in dollars, even when neither the lender nor the borrower is American. Nearly 90 percent of bank-financed international transactions are conducted in dollars.

Growing demand for dollars adds sting to Mr. Trump’s sanctions and tariff threats against China, Mexico, Europe, Iran and multiple other targets. When he vows to sever access to American financing for anyone doing business with Iran, the world has no choice but to listen since it is nearly impossible to conduct international business without involving an American bank, given the dollar’s dominance.

At this critical juncture, any deliberate government campaign to weaken the dollar is likely to backfire against would-be patriots and nationalists by damaging the economy and undermining one of the last thriving symbols of postwar American hegemony.

Ruchir Sharma, author of “The Rise and Fall of Nations: Forces of Change in the Post-Crisis World,” is the chief global strategist at Morgan Stanley Investment Management and a contributing opinion writer.

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