Some of the biggest tax law changes in 30 years took effect on Jan. 1, and American workers have already started to see the impact of new tax provisions show up in their paychecks. Even as they begin to prepare their tax returns for the 2017 tax year, taxpayers hope that 2018 will bring even bigger savings.

In the State of the Union address on Tuesday night, President Trump referred to the accomplishments of tax reform, making the following statement:

A typical family of four making $75,000 will see their tax bill reduced by $2,000, slashing their tax bill in half.

Let's look more closely at the math behind that claim.

White House from the north, with Washington Monument in background.

Image source: Getty Images.

What is a typical American family?

Obviously, President Trump's speech didn't go into elaborate detail about the assumptions he made in working through a typical American family's tax situation. It's reasonable to guess that the president was referring to a married couple earning a total of $75,000 from regular employment, with two children of ages that would make them eligible for the child tax credit. Because the president had referred to the increased standard deduction immediately prior to the comment, we'll look at a situation in which the taxpayers take the standard deduction both in 2017 and in 2018.

Below are some simple calculations on this typical American family's tax liability:

Item

2017 Tax Year

2018 Tax Year

Gross income

$75,000

$75,000

Standard deduction

($12,700)

($24,000)

Personal exemption

($16,200)

N/A

Taxable income

$46,100

$51,000

Tentative tax

$5,983

$5,739

Tax credits

$2,000

$4,000

Net tax owed

$3,983

$1,739

Calculations by author based on IRS rules.

In this case, the president's claim is true. The family's tax liability falls by roughly $2,250, or more than half from projected 2017 tax liability.

You can see that the loss of personal exemptions more than offsets the increase in the standard deduction, leaving the taxpayer with higher taxable income in 2018. Yet the lower tax rates under tax reform result into a reduced tentative tax owed. Then, the biggest downward impact on this family's tax bill comes from the rise in the child tax credit from $1,000 per child to $2,000. That credit is crucial in producing the overall tax savings that this family will see.

What if you have no children?

To be fair, the president's example referred specifically to families of four, with a strong implication of two married adults and two children. However, others will be interested to see how they fare under tax reform, including those who aren't parents.

Let's look at a similarly situated couple with no children. Again, this couple takes the standard deduction and gets all their income from regular employment. The calculations are below:

Item

2017 Tax Year

2018 Tax Year

Gross income

$75,000

$75,000

Standard deduction

($12,750)

($24,000)

Personal exemptions

($8,100)

N/A

Taxable income

$54,150

$51,000

Tax

$7,190

$5,739

Calculations by author based on IRS rules.

Here, the difference in tax is about $1,450. The couple with no children has fewer personal exemptions, so the boost in the standard deduction results in a greater reduction in taxable income. The lower rates then produce the remainder of the tax savings. $1,450 is a significant reduction, but it's far from a 50% tax cut in this case.

Lots of variables in tax reform

The problem with any analysis of this type is that different assumptions can lead to wildly different results. Key issues that have dramatic impacts on tax liability came up numerous times during the debate over tax reform.

For instance, those who itemize deductions could see correspondingly less savings under tax reform, because the increased standard deduction could have little or no impact on the amount by which their gross income is reduced to arrive at taxable income. Indeed, the elimination of some itemized deductions and the limitation of popular provisions like the state and local tax deduction could lead some taxpayers to have a smaller deduction than they enjoyed under previous law. Just how big a tax hike that proves to be will depend on your specific amounts of income and deductions and the corresponding tax rate.

The type and size of your household also has a huge impact. Typical single filers with no children and incomes of $75,000 could see a tax cut of about $3,500, or almost 30%, due to the higher standard deduction and lower tax rates. For larger households, the key question is whether the $1,000 boost in the child tax credit outweighs the loss of the $4,050 personal exemption, which depends on your tax bracket and other aspects of your tax situation.

President Trump's claim about a typical family seeing their tax bill cut in half was true, as long as we take into account the implicit assumptions made in the statement about what a typical family is. Your savings will vary, but there are many people who will see substantial reductions in what they owe the IRS in 2018 compared with what they pay this tax season.

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