President Donald Trump’s trade war provided the kind of real-world experiment that practitioners of the dismal science so desperately crave, but the results weren’t all that different from what their econometric models predict.

In a new paper, “The Impact of the 2018 Trade War on U.S. Prices and Welfare,” economists Mary Amiti of the Federal Reserve Bank of New York, Stephen J. Redding of Princeton University and David Weinstein of Columbia University document what economists have told us for decades: that tariffs are a tax on the consumer.

Trump may say, and believe, that “billions of dollars will soon be pouring into our Treasury from taxes that China is paying for us,” but China isn’t paying the taxes. U.S. consumers are.

And as for the president’s belief that tariffs will “cure” the nation’s trade deficit, which he sees as a sign of weakness, today’s data suggest otherwise. (More on that later.)

The study found that the waves of tariffs throughout 2018 resulted in “substantial increases” in the prices of intermediate and final goods, the cost of which was borne entirely by U.S. consumers. There was little improvement in the “terms of trade,” which means exporters didn’t lower their pre-tariff prices. And the higher price of imports enabled U.S. producers to raise their prices.

What’s more, the tariffs introduced inefficiencies by disrupting supply-chain networks. And the customs duties were insufficient to offset the loss to consumers.

What the tariffs imposed on products ranging from solar panels to washing machines to steel and aluminum to some $250 billion of Chinese goods did offer was an opportunity to test well-established theory: a kind of “natural experiment for evaluating the effects of trade policy.”

How so? For starters, the tariffs weren’t anticipated. Trump wasn’t expected to win the 2016 presidential election, so there was no front-running by those concerned about a lifelong trade protectionist assuming the presidency and imposing his fixation on the nation and its trading partners.

Second, the large size of the tariffs — 20%-50% on washing machines and up to 25% on some Chinese goods — made it easy to discern their impact.

For example, the consumer price index for major appliances had been falling for years. Once a hefty tariff was imposed on washing machines, the CPI for that category of goods started to rise.

There was little change in the prices of goods unaffected by tariffs and “large increases” in the prices of those subjected to tariffs, with the magnitude of the price increases matching the tariff rate.

Why is the effect of tariffs so hard for Trump to understand? While the president has managed to surround himself with a select group of trade protectionists, it’s scary to think that none of them understands how tariffs work.

A tariff, quite simply, is a tax placed on an import. The importer — in most cases, a middleman — forks over the tariff to the U.S. government and passes along the full cost to the firms with whom he contracts.

And what do those middlemen do? They can eat the additional cost, lowering their profit margins, which is unlikely for more than a brief period as they try to retain market share. They can try to negotiate a better deal with the foreign exporter. Or they can find alternate sources the goods they sell, which takes time and costs money.

In the second and third instances, the exporter may suffer consequences, but in no way is China paying the tariffs, as Trump constantly insists.

And while customs duties rose by $7 billion, or 19%, in fiscal 2018 in part because of new tariffs imposed by the administration, all of that revenue was used to compensate farmers for losses due to China’s retaliatory tariffs on U.S. exports, such as soybeans.

For the year as a whole, Amiti, Redding and Weinstein calculate that the tariffs cost U.S. consumers and businesses $4.1 billion a month: $3 billion in tax costs and $1.4 billion in deadweight, or efficiency, losses. That’s still relatively small in a $21 trillion economy, but given his faith in tariffs as a negotiating tool, Trump has other countries (India) and goods (autos) in his sights. (Tariffs inflict harm while we wait for the negotiations to bear fruit.)

If the tariffs remain in place, the actual and anticipated reorganization of supply chains to avoid them would affect an estimated $165 billion in global trade a year, according to the economists.

Another recent study by a quartet of economists confirmed the findings of “a complete pass-through” of the tariffs to U.S. producers and consumers to the tune of $69 billion last year.

And some firms, most notably manufacturing companies, are reassessing their capital spending plans in light of trade tensions, according to a survey by the Atlanta Fed.

None of these outcomes is beneficial. And if Trump’s bottom line is reducing the U.S. trade deficit, which he sees as a sign that the U.S. is “losing” to other nations, he is failing miserably.

The Commerce Department reported today that the U.S. trade deficit rose 12% last year to a 10-year high of $621 billion. A record $891 billion goods deficit — the goods deficit with China set an all-time high of $491 billion — was partially offset by a $270 billion services surplus.

Trade deficits are a function of a nation’s savings and investment.

They tend to be pro-cyclical, rising when economy is doing well and contracting in downturns. Nothing like a good, deep recession to reduce the trade deficit on which the president is fixated.