Donald Trump has created a huge new industry in America for economists and scribes desperate to prove the president was wrong when he declared “trade wars are good, and easy to win.”

Trump’s repeated claims that China is paying for the tariffs imposed on goods the Asian nation exports to the United States have elicited derision and widespread claims that “tariffs tax consumers.” But until recently, the anti-tariff forces were handicapped by the fact that consumer prices in the U.S. have not shown many signs of being pushed up by tariffs.

On Saturday, however, economists from Columbia, Princeton, and the New York Federal Reserve released a paper, “The Impact of the 2018 Trade War on U.S. Prices and Welfare,” that purported to show that foreign exporters paid none of the tariffs and instead the costs fell mostly on U.S. consumers. Paul Krugman of the New York Times pronounced it “a beautiful piece of work.”

Fortunately, the paper suffers from three major flaws, one of them fatal. As it turns out, the paper does not show that tariffs get passed on to consumers.

The U.S. government regularly collects data on the value and quantities of imports. So the economists derived unit prices of imports hit by tariffs by simply dividing the value by the quantity. What they found is that, even though the quantities of imports subject to tariffs had fallen, the unit prices had not.

Since someone must be paying the tariffs, the economists decided that U.S. importers must be paying them—and then passing on the costs to consumers. Note that they do not have direct evidence of either of these things. The idea that the importers are paying is just an inference from the unit price data and the idea that the tariffs are passed through to consumers is based on nothing more than an assumption that higher producer prices must get passed along to consumers.

The first problem with the study is that it is too reliant on reported import prices—and these are not very reliable, especially in the immediate aftermath of tariff changes.

Import values are supposed to be based on the actual prices paid by importers to foreign manufacturers, less the cost of insurance and shipping. But around one-quarter of all imports from China are valued under a different methodology because they are transactions between related parties—foreign arms of multinational corporations. The official values of these imports tend to be sticky because they have to be estimated according to various customs rules because the U.S. government is wary that companies will underprice imports to dodge any duties imposed. This puts upward pressure on reported values, at least temporarily.

It’s hard to tell from the official data how much of the stability in unit price the economists detected was due to related-party stickiness. But since the alternative valuation applies to around a quarter of imports from China—and only half of imports are subject to the new tariffs—the effect could be quite large. And it is clear from the paper that the economists did not even attempt to measure this. There’s no indication that they are even aware of the problem.

The second problem is that the economists missed a very important way China is paying for the tariffs: in lost sales. Imports of tariffed goods fell sharply, according to the paper. This is partly because U.S. consumers bought more items produced domestically, and partly because multinationals shifted their supply chains to avoid the tariffs, moving production from China to Vietnam or Mexico. These lost sales are a cost to China—an indication that China is paying a price for the tariffs.

The third flaw, however, is the killer. The economists assume that the price of tariffs paid by importers are fully passed on to consumers. But the Producer Price Index data show that has not happened. Instead, American businesses—their margins inflated by the huge Trump tax cut—have absorbed the costs of tariffs. They’ve screeched loudly about the tariffs pushing up their costs, so it should hardly be news to anyone.

It is quite odd for anyone to assume that tariffs, which are just taxes, get fully passed on to consumers. Almost no one assumes this about other taxes, whether we’re talking about corporate income taxes, taxes on corporate jets, taxes on dividends, or taxes on financial transactions. To a first approximation, no one on earth believes that the Trump corporate tax cut means that consumers pay lower prices. So why would a tax hike—in the form of a tariff hike—mean they pay higher prices?

Prices last year grew by less than the 2 percent targeted by the Federal Reserve, which at a first estimation is a good sign that anyone claiming consumers are paying for tariffs is wrong. The most likely effect of a tariff on prices is simply to shift some consumer prices up and some down, with a great deal of the tax absorbed by producers, middlemen, wholesalers, and others before they hit store shelves.

That’s not a mystery. We know very well what sets the price level in the economy, good old supply and demand for goods. Which means tariffs cannot raise consumer prices unless they also raise incomes or force Americans to save less. The additional spending power has to come from somewhere.

Of course, incomes are rising—and at a faster rate than prices. Personal income increased 4.5 percent last year, compared with an increase of 4.4 percent in 2017. Disposable personal income increased 5.0 percent in 2018 compared with an increase of 4.4 percent in 2017. In 2018, personal consumption expenditures increased 4.7 percent, compared with an increase of 4.3 percent in 2017. So income and spending are rising, which means its a good bet that any pricing pressure we do see in the economy is due to rising demand rather than tariffs.

Fortunately, we’re also making more. We’ve added hundreds of thousands of manufacturing jobs despite economists claiming that we were already approaching full employment. There is no sign that, as Krugman claimed, these manufacturing jobs are shifting from one part of the economy to a protected, and less productive sector. In fact, economic output last year grew 3.1 percent, a larger gain than the Fed forecast for 2.5 percent growth before the tariffs were implemented, suggesting a real benefit to on-shoring of U.S. production thanks to tariffs.

Even if the paper were not so deeply flawed, its total estimate of the cost to the U.S. is a net welfare loss of just $17 billion a year, less than 0.1 percent of U.S. GDP. To put it differently, the total “value add” of the Trump administration’s economic policies—deregulation, tax cuts, and trade—far outweighed even the worst-case scenario.