New Zealand's new average and marginal tax rates

This week my ECONS102 class covered taxes, and as luck would have it, today the Government's new tax changes come into effect. As the New Zealand Herald reported yesterday:

The tax cuts the National Party campaigned on will officially take effect tomorrow, with around 3.5 million New Zealanders benefitting, according to Finance Minister Nicola Willis.

Changes from July 31 include an increase in personal income tax thresholds, the extension of the independent earner tax credit (IETC) and an increase to the in-work tax credit and the minimum family tax credit.

I'm going to focus  purely on the changes in personal income tax thresholds, and update a figure I posted back in 2022, which showed the marginal tax rate and the average tax rate, for taxpayers on different annual incomes. The marginal tax rate is the amount of the next dollar earned that is paid in tax. The proportion of income that a taxpayer pays in tax is called the average tax rate. The marginal tax rate is what people often think about when they think of tax rates. However, for a country that has a progressive income tax, such as New Zealand, the average tax rate is always lower than the marginal tax rate. That's because people on high incomes, with a high marginal tax rate, nevertheless have paid a low marginal tax rate on their first dollars of income.

Anyway, here's the picture of those marginal tax rates and average tax rates. The rates that applied up to yesterday are shown in blue (marginal tax rate) and red (average tax rate). Those are the same lines from my 2022 post. Notice that the marginal tax rate is always higher than the average tax rate (except for very low incomes below $14,000, where they are the same). The new rates applying from today are shown in green (marginal tax rate) and orange (average tax rate).

Notice that changing the personal income tax thresholds shifts the vertical parts of the marginal tax rate schedule to the right (comparing the blue and green lines). That's because the higher rates now kick in at slightly higher incomes.

However, what most people are probably interested in is the change in average tax rates, not the change in marginal tax rates. This is shown by the difference between the red and orange lines. The difference is imperceptible at low incomes, as well as pretty small and decreasing at the highest incomes. It is largest in the middle of the income distribution, which is why the government has sold these changes as helping the 'squeezed middle'.

In fact, the decrease in the average tax rate is largest for those on an annual income of $55,000, [*] where the average tax rate has decreased from 17.31% to 15.86%, a decrease of 1.45 percentage points, or $799.50 per year. That isn't the largest absolute difference in tax paid, which happens at all annual incomes above $78,100, and is equal to $1,042.50 per year. Of course, as a percentage of income, that $1,042.50 is smaller at higher annual incomes, which is why the gap between the red and orange lines gets smaller for higher incomes.

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[*] I only looked at incomes in steps of $2500, and this is closest to the threshold with the biggest step up in the marginal tax rate schedule, which is now $53,500.

Read more:

• Tax cuts, and misinterpreted average and marginal tax rates
• Progressive taxation as an automatic stabiliser

Progressive taxation as an automatic stabiliser

Fiscal policy is the umbrella term used to refer to the government's plans for taxing and spending. It has an impact on the macroeconomy, because government spending becomes income in the hands of households and businesses. So, some people argue that the government can use changes in taxes and spending to counteract the business cycle. This is referred to as countercyclical fiscal policy. Under this approach, when the economy is in recession, the government should tax less and spend more, but when the economy is in an expansion, the government should tax more and spend less. If this worked, then the economic fluctuations of the business cycle would be dampened.

However, it may not be necessary for the government to be quite so interventionist. The economy has some automatic stabilisers, that automatically (hence the name) adjust to increase household incomes when the economy is in recession, and decrease when the economy is in expansion. One example of an automatic stabiliser is the unemployment benefit. In a recession, more people are unemployed and this increases the number of unemployment benefit claims, reducing somewhat the negative impact of the high unemployment on spending. When the economy is in expansion, fewer people are unemployed and there are fewer unemployment benefit claims, reducing the amount of stimulus provided by the unemployment benefits.

To be fair, the unemployment benefit doesn't provide enough stabilisation on its own to substantially reduce the size of business cycle fluctuations. But the unemployment benefit is not the only automatic stabiliser. Progressive income taxation may be another.

A progressive income tax is one where the marginal tax rate (the amount of the next dollar that is paid in tax) is greater than the average tax rate (the proportion of total income that is paid in tax). A typical tax schedule that leads to progressive income tax is a graduated income tax, like that employed in New Zealand, where there are specific income bands that have different marginal tax rates, with higher marginal tax rates within higher income bands.

That looks something like the following graph, which uses the current income tax rates for New Zealand. The blue solid line shows the marginal tax rate, and the red dotted line shows the average tax rate. Notice that the marginal tax rates jumps up at regular intervals (this is a graduated income tax). Above the first income tax threshold, the average tax rate is always below the marginal tax rate. This is a progressive income tax. Also, notice that no one pays 39 percent income tax (which is a point that I have made before). Even at the highest income shown in the diagram ($250,000), the average tax rate is just over 31 percent. That's because, even for those at the highest incomes, their first $14,000 is taxed at 10.5 percent, the next $34,000 at 17.5 percent, and so on. Only each dollar above $180,000 in income attracts a marginal tax rate of 39 percent.

Anyway, coming back to progressive taxation as an automatic stabiliser, when the economy is in an expansion, incomes rise, and more taxpayers will find themselves paying more tax (because they move to the right along the diagram above). In fact, because of the progressive nature of the tax system, the percentage change in taxes is bigger than the percentage change in income. A taxpayer moving from $50,000 to $55,000 in income (a 10% increase) will go from paying $8,020 in tax to paying $9,520 (an 18.7 percent increase). This also works in reverse. When the economy is in a recession, incomes fall, and more taxpayers will find themselves paying less tax. So, a taxpayer moving from $50,000 to $45,000 in income (a 10% decrease) will go from paying $8,020 in tax to paying $6,895 (a 14.0 percent decrease). The same applies to other levels of incomes and income changes that we might consider.

So, when the economy is in recession, progressive taxation removes less from household incomes, and when the economy is in expansion, progressive taxation removes more from household incomes. This will act to reduce the size of economic fluctuations of the business cycle, making progressive taxation an automatic stabiliser.

[HT: John Quiggin, in his book Economics in Two Lessons, which I reviewed here]

Read more:

• Tax cuts, and misinterpreted average and marginal tax rates

Evaluating the fiscal cost of tax cuts

As reported in the New Zealand Herald today, the Taxpayers' Union released a new report today titled "5 Options for Tax Relief in 2017". I haven't had a chance to read the report in great detail, but here's what the Herald had to say:

The average New Zealand worker is paying $483 a year more in tax because income brackets have not been adjusted with inflation, a new report by a right-wing lobby group claims...

In an effort to put pressure on the National-led Government ahead of May's Budget, the report assumes $3 billion is available for tax relief in 2017/18.

The report outlines five different options for how those tax cuts could be divvied out.

They are:

• A tax-free threshold of up to $13,000. The report states this would save taxpayers $1295 a year, for those earning more than $13,000.

• Cutting the marginal tax rate for earnings between $48,001 and $70,000 to 17.5 per cent, and increasing the 10.5 per cent threshold from $12,000 to $24,000.

The report says this would particularly benefit middle income earners, giving the example of a $4000 a year saving for a dual-income household with a combined income of $100,000.

• Cutting tax rates for high income earners by eliminating the top tax bracket and reducing the rate above $48,001 to 26 per cent, and slashing company and trust tax rates to 26 per cent.

Those measures would save a person earning a $120,000 salary more than $4300 a year. A low income earner would get no benefit, while the average earner would save just $360 a year.

• Increasing the income thresholds of each tax bracket without adjusting any of the tax rates.

• Reducing the company tax rate from 28 per cent to 13 per cent, at a cost of $2.88 billion.

The report stated that an "average worker" on $57,000 is paying $483 a year more in tax than they would had income tax thresholds been adjusted for inflation since 2010.

Back in February in another article about tax cuts, Brian Fallow pointed us to this handy tool on the Treasury website: The Personal Income Tax Revenue Estimate Tool. It's an Excel-based tool (it would be even cooler if it were fully online) that allows us to evaluate the impact of changes in the tax brackets or marginal income tax rates (the proportion of the next dollar that would be paid in income tax) on total tax revenue (from personal income tax).

I had a bit of a play with the tool and the assumptions above, and here's what it came up with:

• The tax-free threshold of up to $13,000 would reduce personal income tax revenue by $3.35 billion
• Cutting the marginal tax rate for earnings between $48,001 and $70,000 to 17.5 per cent, and increasing the 10.5 per cent threshold from $12,000 to $24,000 would reduce personal income tax revenue by $3.46 billion
• Eliminating the top tax bracket and reducing the rate above $48,001 to 26 per cent would reduce personal income tax revenue by $2.49 billion (and reducing company and trust tax rates to 26 percent would reduce taxes paid by those entities as well) 
• Increasing the income thresholds of each tax bracket without adjusting any of the tax rates (as per their report) would reduce personal income tax revenue by $3.46 billion
• Reducing the company tax rate can't be evaluated using the PITRE tool.

I leave it up to you to decide whether these different tax changes, each costing around $3-3.5 billion according to the PITRE tool, are affordable and worthwhile. The estimates should be taken with some caution however (and the PITRE tool even warns against making large changes to the tax rates and bracket thresholds). Whenever marginal tax rates change there are a raft of effective marginal tax rate changes that affect incentives to work (or not work), that cannot easily be evaluated with a simple tool such as this. However, I do encourage you to download and play around with the tool, especially if you want to see how marginal and average tax rates work, and the effects of changing them (slightly!).

Tax cuts, and misinterpreted average and marginal tax rates

Many, many people don't understand the difference between average and marginal tax rates. Articles like this one by Leicester Gouwland don't help:

The bulk of the default tax collected is from people who have moved from the 17.5 per cent bracket to the 30 per cent bracket, that is a 71 per cent increase in tax.

The people who have moved from the 10.5 per cent bracket to the 17.5 per cent have suffered a 66 per cent increase in tax, however, if they now earn more than $24,000, they qualify for the independent earner rebate.

Neither of those two statements is correct. To see why, let's take a step back first. The average (income) tax rate for a taxpayer is the tax that they pay divided by their income. So, if a taxpayer have income of $50,000 and pay $8,020 in tax, their average tax rate is 16.04% (8,020 / 50,000). The marginal tax rate is the proportion of the next dollar they earn that would be paid in tax.

Most income tax systems are described in terms of marginal tax rates, as Gouwland does early in his article for New Zealand:

The current tax brackets on personal income are; 10.5 per cent for income up to $14,000; 17.5 per cent for income up to $48,000; 30 per cent for income up to $70,000; and then 33 per cent for any income more than $70,000.

So, for our taxpayer that has income of $50,000, their marginal tax rate (the tax rate they would pay on the next dollar they earn) is 30%, even though their average tax rate is only 16.04%.

Now, this is where most people go wrong. A person who moves tax brackets doesn't face a huge increase in their average tax rate, only their marginal tax rate. It's not correct to say that, for someone who moves "from the 17.5 per cent bracket to the 30 per cent, that is a 71 per cent increase in tax". To illustrate, let's take a taxpayer who was previously earning $45,000 (in the 17.5 per cent tax bracket) and give them a pay rise to $50,000 (in the 30 per cent tax bracket). Does their tax payment go up by 71% (as Gouwland suggests)? Hell no. It only goes up by 16.3%, from $6,895 to $8,020. [*] That's still a big increase, but it's certainly not 71%! And remember that their before-tax income has gone up by 11.1% as well.

Similarly, has someone who has moved "from the 10.5 per cent bracket to the 17.5 per cent ...suffered a 66 per cent increase in tax"? Let's take a taxpayer who was previous earning $12,000 (in the 10.5 per cent tax bracket), and increase their income to $16,000 (in the 17.5 per cent tax bracket). Their tax payment goes from $1,260 to $1,820, an increase of 44.4% (but in the context of a 33.3% increase in pre-tax income).

So, more care is needed in interpreting average and marginal tax rates, and articles like Gouwland's certainly don't help.

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[*] The tax paid by a taxpayer with an income of $45,000 is calculated as [$14,000 x 0.105] + [($45,000 - $14,000) x 0.175] = $6,895. The tax paid by a taxpayer with an income of $50,000 is calculated as [$14,000 x 0.105] + [($48,000 - $14,000) x 0.175] + [($50,000 - $48,000) x 0.3] = $8,020.

[**] The tax paid by a taxpayer with an income of $12,000 is calculated as [$12,000 x 0.105] = $1,260. The tax paid by a taxpayer with an income of $16,000 is calculated as [$14,000 x 0.105] + [($16,000 - $14,000) x 0.175] = $1,820.