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Republicans have a math problem.

They're on the verge of passing a tax cut that would cost $1.5 trillion over the next 10 years, but they don't want it to cost more than $500 billion. That, apparently, is where their self-styled “deficit hawks,” whose votes the party can't afford to lose, draw the line between fiscal prudence and fiscal folly.

The question, then, is how to find $1 trillion worth of savings. And the answer, of course, is with magic. More specifically, with the kind of wishful thinking that says tax cuts can completely pay for themselves by making the economy grow so much more. It's something that former George W. Bush adviser Greg Mankiw once said only “charlatans and cranks” believe, which doesn't speak well of the current composition of the Republican Party — because most of them believe it today. Indeed, President Trump's top economic adviser, Gary Cohn, said that “we can pay for the entire tax cut through growth.” Treasury Secretary Steven Mnuchin agreed that “the plan will pay for itself with growth.” Sen. John Thune (R-S.D.) said that even “a modest amount of economic growth” could “cover the cost of this bill.” And White House budget director Mick Mulvaney went so far as to say he thinks it “actually generates money.”

No actual expert agrees. The nonpartisan Tax Policy Center, for one, thinks the Senate plan would barely make the economy grow more over the next decade — enough to pay for only $179 billion of its $1.4 trillion cost. The Penn Wharton Budget Model, for another, estimates that it would add somewhere between 0.3 percent and 0.8 percent to growth over the next 10 years, offsetting $100 billion to $275 billion of its $1.3 trillion cost. And, as we found out Thursday, the official budget scorekeepers at the nonpartisan Joint Committee on Taxation are similarly pessimistic about the prospects of self-financing tax cuts. They estimate that growth would cover only $408 billion of the Senate plan's $1.4 trillion price tag.

That's left Republicans looking for somebody, anybody, who will tell them that their tax cuts wouldn't cost as much as they almost certainly would. And that is where the conservative Tax Foundation comes in. Alone among economic forecasters, it says the Republican tax cuts would increase gross domestic product so much that they wouldn't increase deficits nearly as much as it might seem. In particular, the Tax Foundation thinks that the Senate bill would pay for $1.26 trillion of its $1.78 trillion in tax cuts by generating 3.7 percent more growth — a growth effect that is four to 12 times bigger than in mainstream models.

It's no wonder, then, that the Tax Foundation has become Republicans' favorite think tank. House Speaker Paul D. Ryan has cited it, along with Senate Majority Leader Mitch McConnell and pretty much every other Republican looking for proof that they wouldn't be adding 12 figures' worth of red ink.

Now, anytime somebody is making a much different prediction than everybody else is, it's worth asking why. Which, when it comes to the Tax Foundation, is a much more complicated story than you might think. Before we get to that, though, let's take a minute to talk about economic models. The first thing to understand is that they're not meant to be realistic themselves but to tell us realistic things about the world we live in. The second is that all this has to fit together. You can't assume one thing in one place and a contradictory thing in another. And the third is that different models are built on different assumptions that are appropriate at different times.

Take a middle-of-the-road model like the one the Tax Policy Center uses. It assumes that the United States is what's known as a big open economy — meaning foreign money can come into the country but not flood it — because the United States is, well, a big open economy. It also assumes that unpaid-for tax cuts end up slowing the economy down, since, in the long run, bigger deficits tend to mean higher interest rates. And finally it assumes that the Federal Reserve will do its job and choke off faster growth if inflation rises above its 2 percent target.

The Tax Foundation, on the other hand, doesn't assume any of these things. It starts from the premise that the United States isn't a big open economy like it actually is, but rather a small open one like Ireland. How does that change things? Well, in that case, corporate tax cuts would make foreign investors send mountains of money into the country until, very quickly, the only investments left were ones that offered the same after-tax return as everywhere else in the world. On top of that, it doesn't think tax cuts could ever be bad for growth by leading to, say, higher debt or higher interest rates from the Fed. Which is to say the Tax Foundation assumes that tax cuts have fewer costs and bigger benefits than anybody else does.

But the Tax Foundation isn't just getting more optimistic results because it's making more optimistic assumptions. Even then, it's hard to figure how it gets its numbers. “I've always been puzzled by their model,” Kent Smetters, a former Bush economist who is now the director of the Penn Wharton Budget Model, told me, “but there aren't enough details for me to understand it.” Part of it, as Greg Leiserson, the tax director at the Washington Center for Equitable Growth, has pointed out, is that the Tax Foundation made a number of mistakes, one of which it's since corrected. But there's also what seems to be a more fundamental problem: The foundation seems to be assuming things that shouldn't be assumed together. Now, I say “seems,” because I asked the foundation about all this, and it still isn't clear exactly what's going on. But there are a few red flags that suggest something is.

The first one has to do with the estate tax. The Tax Foundation thinks getting rid of it would help quite a bit — it's responsible for 0.7 percentage points of the 3.5 points of extra growth it says the House plan would produce — but it's hard to see how that could be, given the model the foundation is using. Think about it like this. You can say taxing uber-wealthy heirs is bad for growth, because they're the ones who have the money to make the investments we need. What you can't do, though, is say that about a small open economy. In that case, people overseas would step in to invest if people at home couldn't. So repealing the estate tax shouldn't matter. The economy should grow the same either way.

The second red flag is how a corporate tax cut would even work. Remember, the small open economy model says this would make a lot of foreign money come in. So you'd expect the share of investment income going to foreigners to go up a lot too. (That's why Ireland's super-low corporate tax rate has helped its GDP stats a lot more than its people: A big chunk of the benefits of foreign investment have to be paid back to, yes, foreign investors.) The Tax Foundation, though, assumes that the share of investment income going to foreigners wouldn't increase at all, even though the share of investment coming from foreigners would. The result is that corporate tax cuts look a lot better for Americans than they actually would be.

What's going on here? Well, we can't say for sure, but it seems like the Tax Foundation has taken a simple idea and applied it in ways that don't quite work together. That idea is that anything that raises taxes on savings — corporate taxes, capital gains taxes, dividend taxes or the estate tax — hurts growth, and anything that cuts them helps it. Where the foundation seems to run into trouble, though, is in always using very strong assumptions about how much these things hurt. The problem is that the assumptions built into the idea that the corporate tax is particularly bad for growth are different from the ones that tell you the estate tax is. So, to try to make it all fit together, the foundation seems to come up with some ad hoc justifications for why things that normally don't go together should here. Maybe that's a study it says backs up its ideas, or a historical relationship, or something like that. What it isn't, though, is a formal model. I asked the foundation if it did that — if it could mathematically reconcile these things — and it doesn't.

The Tax Foundation, for its part, insisted that its model is “best described as a small open economy,” since "'small' is a relative term” and “our share of the world economy has fallen” from 40 percent in 1960 to 25 percent today, with “significant financial flows from other parts of the world” now coming in. It also told me that “all of the assumptions laid out are neoclassical assumptions” that are “a result of an open economy model.” In the specific case of the estate tax, it thinks getting rid of it would still help, even in an open economy model, because it's like a tax businesses have to pay in addition to the corporate tax. But more broadly, its analysts use “comparative statistics,” which “only estimates long-run effects,” and then “generally assume that the economic effects of tax changes take ten years to fully phase in” because, in part, that's what they think has historically been the case.

In any case, this is just another reminder of the value of nonpartisan scorekeepers. You shouldn't rewrite the tax code based on the best of best-case scenarios or on the promise of a secret analysis that supposedly vindicates you. That's what Treasury Secretary Mnuchin did, claiming he had a study showing that the tax cuts really would pay for themselves, before the New York Times reported Thursday that this wasn't true. It turns out there is no study.

Instead, Republicans might want to try inviting experts to answer their questions — they could even call it a “hearing” — or waiting for the budget scorekeepers to run the numbers, or, heck, even writing the bill first before rushing for a vote. It might sound quaint, but the Reagan administration did this for two years when it was working on tax reform. Republicans today have barely done it for two weeks.

It's almost like they want to pass the bill before they find out how much it would actually cost — not that would stop most of them.

Being a fiscal conservative means never having to pay for your tax cuts.