Another prominent critic of a "border adjustment tax" emerged Tuesday: the president of the New York Federal Reserve.

Bill Dudley was asked by Macy's CEO Terry Lundgren at a meeting of the National Retail Federation trade group what he thinks of the idea of a border adjustment tax, which involves taxing imports at 20 percent, while making U.S. exports tax-free.

GOP leaders in the House of Representatives are pushing the tax idea as part of their "Better Way" blueprint. The biggest U.S. retailers, which are largely in the business of shipping in products from Asia and selling them to American consumers, is strongly opposed to border adjusted taxes.

The New York Fed president agreed that such taxes would mark a "pretty dramatic change."

"I think that it will lead to a lot of changes in the value of the dollar, the price of imported goods in the U.S., and I'm not sure that would all happen very smoothly," Dudley said. "I also think there could be a lot of unintended consequences."

Most supporters of the tax argue that the dollar will strengthen so much as a result of border adjustment that imports will in effect become cheaper or at least remain the same — and therefore, consumer prices will not increase.

But Dudley indicated skepticism about that idea.

"I'm not of the view that import prices would go up 10 percent, the dollar would appreciate by exactly 10 percent, so that the value that retailers pay for imported goods would be exactly the same in dollar terms," Dudley told the NRF audience.

Lundgren pointed out that for new dollar strength to negate higher import prices, the greenback would have to increase specifically against the currencies of countries that make the products sold by American retailers.

Economists who have looked at the proposal in the House GOP plan believe it would strengthen the dollar — some by as much as 20 to 25 percent,

If true, Dudley said, that would hurt tourism to the United States: "Fewer people would come to the U.S. as tourists; more of us would go abroad. It would change the relative attractiveness in investing in U.S. financial assets versus investing in foreign assets."

Dudley's comments come after President-elect Donald Trump called the border adjustment tax idea "too complicated" in a Wall Street journal report over the long weekend.

In the same interview, Trump said the dollar is "too strong."

His comments sent the U.S. currency skidding Tuesday .

Stocks of retailers, meanwhile, rose sharply Tuesday.

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