Donald Trump’s pitch for his tax plan is simple: Middle-class families will pay less.

The Trump campaign site, for instance, promises that his plan will cut taxes for a married couple with two kids, $50,000 in earnings, and $8,000 in child care expenses by a whopping 35 percent. Not bad, huh? Even though the plan concentrates benefits among the rich, it’s hard for a middle-class family to get annoyed at their tax bill falling by over a third.

The only problem: This is a lie.

According to a paper by NYU Law’s Lily Batchelder, such a family would only see their taxes go down by $93, or 0.2 percent of their income. Trump is exaggerating the size of the cut dramatically.

But it’s worse than that. Three recent changes to Trump’s plan, which limit deductions and increase rates relative to the original version, combine to generate significant tax increases for wide swaths of the middle class. Batchelder conservatively estimates that 25 million individuals and 15 million children will see their taxes go up. That's about 20 percent of households with minor children at home, and includes more than half of all single parents.

The Trump campaign has, naturally, vociferously disputed Batchelder’s findings. But her rebuttals to the campaign’s complaints are persuasive, and analysts at the right-leaning Tax Foundation have come to similar conclusions.

As the evidence stands currently, it appears that Trump has, by accident more than anything, found himself with a tax plan that would raise taxes meaningfully on many middle-class families.

Why Trump’s plan raises taxes on certain middle-class families

Batchelder’s analysis is only valid because of a number of relatively recent changes to Trump’s tax plan, all taken with the goal of bringing down its extravagantly high price tag:

The first tax plan kept the bottom income tax rate at 10 percent, the same as under current law. But Trump then changed it to make the bottom rate 12 percent. That raises taxes on everyone with a positive tax burden, all else being equal. This is offset — and then some — for rich families by lower rates higher up the income scale (like a 33 percent top bracket, down from 39.6), but it's hardly offset at all for many middle-class families. Trump's initial plan also saw a dramatic increase in the standard deduction, from $12,600 to $50,000 for married couples. Trump would've kept the personal exemption, an additional deduction that all taxpayers can claim for themselves and their family, at its current level of $4,050. But his updated plan not only cut the standard deduction to $30,000 for married couples, it also eliminated personal exemptions entirely. So a family of five claiming a personal exemption for each would actually be worse off under Trump’s changes, as five times $4,050 plus $12,600 is greater than $30,000. Trump’s initial plan left head-of-household filing status, which effectively lowers taxes for unmarried individuals caring for an adult or child dependent, untouched. His new plan eliminates it. That puts middle-class single parents, and single adults caring for a parent or relative, in a bind.

You might think that Trump's proposed deduction for child care costs would mitigate some of these tax increases. But as Batchelder notes, that deduction isn't very valuable for non-rich people. It's less valuable the lower your tax bracket is, and you have to choose between it and the child and dependent care tax credit, which is more valuable for most middle-class families.

Batchelder provides several examples of families that would see their taxes go up under Trump’s plan. The biggest hikes number in the thousands of dollars, and are concentrated among single parents:

A single parent with $75,000 in earnings, two children in school, and no child care costs (because the kids are in school) would pay $2,440 more .

. A single parent with $50,000 in earnings, three children in school, and child care costs of less than $6,000 would pay $1,188 more .

. A married couple with $50,000 in earnings, two kids in school, and no child care costs would pay $150 more because of the bottom bracket's increase from 10 to 12 percent.

Batchelder helpfully summarizes this in two tables, one for single parents:

And one for married couples:

Who’s affected depends on how many children they have and how much they have in child care costs; married families with only one child probably won’t face a tax increase, for example. That said, all but a small handful of single-parent families with non-exorbitant child care costs would be worse off.

Trump’s campaign disputes the analysis, but the objections don’t hold up

Batchelder is hardly a neutral in this election; she was the chief Democratic tax counsel on the Senate Finance Committee from 2010 to 2014, and a deputy director of the National Economic Council in the Obama White House from 2014 to 2015.

But she’s also a hugely respected tax analyst who is taken seriously by experts on both sides of the aisle. Tellingly, Kyle Pomerleau, of the right-leaning Tax Foundation, says the group was able to replicate Batchelder’s findings:

.@lilybatch We were able to replicate many of the numbers in the report. The results seem reasonable to me. — Kyle Pomerleau (@kpomerleau) September 26, 2016

The left-leaning Citizens for Tax Justice, similarly, found that the new plan would raise taxes for a significant number of middle-class Americans.

Naturally, however, the Trump campaign claims the analysis is off base. They offered four objections to the Washington Post’s Jim Tankersley, all of which Batchelder has already rebutted on her Twitter account:

1) The Trump camp claims that Batchelder ignores a provision in Trump's plan that offers low-income parents who put money into child and dependent care savings accounts a government-funded match of up to $500. But as Batchelder notes, this only applies to low-income families, not the middle class, the group that stands to see taxes go up under the Trump plan. Furthermore, experience with similar programs suggests that very few low-income families will take advantage of this match:

The Trump campaign has more criticisms of my paper: https://t.co/0hARv9rx2H. The problems with their first argument: pic.twitter.com/5AjwWr8nCu — Lily Batchelder (@lilybatch) September 25, 2016

2) The Trump campaign claims that Batchelder ignores the repeal of a tax on investments included in Obamacare. But this tax only applies to income over $250,000 for married filers, so there's no chance a middle-class family would pay it.

3) Trump's aides also say that Batchelder didn't take into account the fact that families will change their decisions on whether to itemize in response to the tax reform plan. But this is a red herring; all the tax increases Trump includes apply equally to people taking the standard deduction or itemizing:

The problems with the Trump campaign’s second criticism of my paper at https://t.co/4IqCXFqlvk. pic.twitter.com/cEotvNkj0U — Lily Batchelder (@lilybatch) September 25, 2016

4) The Trump camp attacks the Batchelder estimates for not assuming that Trump’s plan will increase economic growth. This is silly; there’s huge debate over the effect of taxes on growth, and it’s perfectly appropriate to do estimates of how changes in taxes would affect families in the short-run, before any miraculous growth effects occur.

5) My favorite objection from Trump’s people was their claim that they’ll just tell Congress to write the law in such a way that middle-class people don’t see taxes increase. That sounds like a decent enough idea, but it requires junking the actual plan Trump has proposed:

The problems with the Trump campaign’s fourth criticism of my paper at https://t.co/4IqCXFqlvk. pic.twitter.com/rMCgMUMnqB — Lily Batchelder (@lilybatch) September 25, 2016

Additionally, Batchelder notes that there are a number of ways in which her estimates are too conservative; they ignore a number of key ways in which Trump could wind up raising yet more people’s taxes, or lead to bigger tax hikes for middle-class families with kids than the ones Batchelder estimates:

Another problem with the Trump campaign’s criticisms is they ignore all the ways my estimates are underestimates: pic.twitter.com/Ay1GLodoGP — Lily Batchelder (@lilybatch) September 25, 2016

It’s important not to overstate what Batchelder found here. Many middle-class families would still see taxes decline, and the larger problem with the Trump tax cuts is that they would have to be financed either through a massive expansion of the national debt or by dramatically cutting the safety net and entitlement programs for the elderly.

But it certainly does seem like a large chunk of the middle class will pay more under his proposal. More than anything, that’s a sign of the striking sloppiness with which Trump has approached policy questions this whole campaign. These are problems that ought to have been worked out before the tax plan was announced — especially given that it was his third tax plan of the campaign. These problems weren’t worked out, though, because Trump does not appear to have a professional policy shop to speak of.

Correction: The first version of this article equated a percentage change in a tax bill to change in after-tax income; it has been corrected.

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