# How many households pay net tax in Australia?

**Posted:**October 5, 2014

**Filed under:**Uncategorized 1 Comment

I managed to miss an article by Professor Richard Holden the other day about tax reform. Things didn’t start off well when Professor Holden advised of the need for a ‘national discussion’ about tax reform. (I’ll bring the stale biscuits and teabags; you bring the chin-strokey phrases.) Holden contends that Australia’s tax system is plenty progressive already:

First, let’s look at the baseline. Australia has a very progressive income-taxation system. The top 10 per cent of earners pay 46 per cent of total income taxes. The top 2 per cent of earners pay 26; the top 1 per cent pay nearly 18 per cent. The bottom 20 per cent pay 2.5 per cent. This makes Australia’s income-tax system among the most progressive in the world.

First of all, it’s important to know what we’re talking about. There is some confusion sometimes about what we mean by ‘progressivity’. In general, it is simply used to mean a system in which the higher your income, the more tax you pay *as a proportion of your income*.

But Professor Holden hasn’t talked about tax rates—he’s talked about tax paid by different income groups *as a proportion of all tax paid*. The two things are related, but they’re not the same thing, and you can’t use evidence about total tax paid as a proportion of the national income tax bill as evidence about the progressivity of income tax. In fact, the proportion of tax paid by an income group is a function not only of the progressivity of the tax rate schedule, but also of the distribution of pretax income.

Consider this simple, rather extreme, stylised example: Imagine there are two people in the economy: Jay Gatsby, who is rich, and Oliver Twist, who is poor. Jay Gatsby earns $1 million in a year, and Oliver Twist earns $10. Now assume that the tax structure is as follows:

**First $5 of income: 50%**

**Every subsequent dollar: 5%**

That this is a *regressive* tax is pretty easy to see. (Oliver Twist’s marginal tax rate is 5%, but his average tax rate is (50% of $5 = $2.50) + (5% of $5 = 25c) divided by $10 =27.5%. His *average* tax rate exceeds his *marginal* tax rate, which is one quick way of checking if a tax is regressive.) But who pays the tax in this economy? Oliver Twist pays $2.75, while Jay Gatsby pays (50% of $5) + (5% of $999,995), which is $50002.25. Clearly Gatsby is paying the vast majority of tax —99.9945% of all tax in this economy—but it’s not because income tax is progressive; it’s because the distribution of income is so unequal.

The two concepts are related (*ceteris paribus*, an increase in the progressivity of a tax will see the share of tax paid by top income earners increase) but they’re not synonymous. There are indeed good reasons for supposing that the Australian system of direct taxation—as in other Anglophonic countries—is quite progressive, but not because of the share of the total income tax bill that is paid by high income earners. But my big gripe comes with another paragraph:

And income taxes are just one component of the broader taxation-benefit system. There are other taxes and benefits designed to redistribute income, such as the Family Tax Benefit, the Schoolkids Bonus and the aged pension. Then there’s a range of ostensibly free services such as healthcare. Finally, there are other taxes, such as the GST.

The ABS estimates that when all of this is factored in, only the top fifth of households ranked by income pay any net tax.

I have numerous problems with this claim, which is one I’ve seen in many other places recently. First of all, let’s see where he’s getting this data from. I *suspect*, though he hasn’t made it clear, that what he’s looking at is the distribution of taxes, transfers and in-kind transfers from the 2009-10 household income survey. If you add up average income and ‘production’ taxes for each quintile and subtract government transfer payments and ‘in-kind payments’ like education and healthcare spending, we get something like Professor Holden’s claim: Now, this is people ranked by their *final income*. That is to say, it ranks households by their income inclusive of welfare and education and health transfers. Then the households are split into five groups, and the average ‘net tax’ paid is computed. This tells us something interesting, but it’s not the only we could rank households. For example, we could rank households based on their *privately earned income* and then perform the same exercise. Doing this, we would see the following averages of ‘net tax’ paid: Now, suddenly, we have the top two quintiles paying net tax on average, instead of just one. So the ranking of households can affect these kind of calculations somewhat dramatically. I also think that the way Professor Holden and I have been calculating this metric called ‘net tax’ is an odd way of looking at what most people would think of when they hear the phrase ‘net tax’. To me, at least, while there is something intuitive about subtracting welfare payments from tax payments to get ‘net tax’ (that is, considering a welfare payment as ‘negative tax’), it seems odd to also subtract the imputed value of health and education spending by considering it ‘negative tax’ as well. It’s also a calculation that will of its nature make it seem as though the poor are paying less ‘net tax’ than the rich, since health and education services are used quite heavily by low-income households (again, ranking by private income rather than final income): What about other government services, like national defence, police and the judicial system? These are also government services, but they’re ones that we may have reason to believe *disproportionately *benefit well-off households, who, possessing more wealth, have more to lose if there were to be a breakdown in law and order. Some people might say that education is different. After all, if the government charged full cost-recovery prices at government-run schools, but gave you a tax credit for the entire amount, then you’d be paying less tax, so in a way, using a free government school is kind of like a negative tax.

To which I respond: isn’t it the same with other government services? National defence is a bit hard to do like this, but fire services, for example, used to be run by insurance companies. What if the government decided to let the private sector deal with the problem of burglary and gave tax credits for insurance premia? You would insure your house, and people with nicer houses and better possessions would have to pay higher premia. So the fact that everyone enjoys the same access to the police now is *exactly* like education in its negative-tax implications, except that the benefits go to the well-off more than to the poor. So I don’t really see why we should deduct these ‘in-kind social transfers’ from tax paid to arrive at ‘net tax.’ What happens if we define net tax as tax paid minus welfare payments? Now we find that it’s only the bottom two quintiles that don’t pay ‘net tax’ on average: So definitions matter. But so too does another little phrase I’ve been sneaking into the above quietly: ‘on average’. While it’s true that, using the definition directly above, the bottom quintile of households pays –$329 a week *on average* of net tax as defined above, it’s also quite obvious that not every household in this group pays this amount of net tax. It’s not even clear that every household in this group pays negative amounts of net tax, or that every household in the top quintile pays positive amounts of net tax. In fact, we have every reason to believe that there are net taxpayers in the bottom quintiles as well as people who pay no net tax in the top quintiles.

But even if we assume that net tax paid is an increasing function of private income, we still encounter problems when we get to the quintiles where net tax paid is close to 0. For example, in what I assume is Professor Holden’s calculation, the fourth quintile pays on average negative $111 in net tax per week. But **even if** net tax paid increases as income does, the negative average in the fourth quintile might obscure quite a lot of net positive taxpayers in the same quintile. To illustrate this, I’ve simulated 100 ‘people’ each of whom pays net tax based on a uniformly random distribution between -100 and 100. I’ve then ordered the households by net tax paid and calculated the average tax for each quintile. Here’s one realisation of this simulation: The mean of the third quintile is negative, which would probably lead someone like Professor Holden to conclude that only ‘two-fifths of households pay any net tax’. But that would be wrong. As you can see, the third quintile average is composed of some household that pay negative tax and some that pay positive tax. In fact, in the above random distribution, 50% of all taxpayers pay net tax, even though *on average* only two quintiles (representing 40% of taxpayers) pay net tax. I also ran a Monte Carlo simulation of the above exercise. I ran the program 10,000 times and for each repetition calculated the percentage of taxpayers who paid net tax as well as the number of quintiles who paid net tax on average. I plotted a histogram and kernel density curve for the number of net taxpayers in the simulation for which there were only two quintiles that paid ‘net tax’ on average: What this shows us, apart from some rather trivial properties of sample means, is that there are some cases where *sixty per cent* of households pay net tax, but only two quintiles, representing 40% of households, pay net tax *on average. *There are also cases where fewer than 40% of households pay net tax, but two quintiles still pay net tax on average. However, in 97.5% of cases, even though only two quintiles paid average positive net tax, more than two fifths of all taxpayers paid positive net tax. (I should emphasise that this is just using made-up data to illustrate a point.)

So when Professor Holden says “The ABS estimates that when all of this is factored in, only the top fifth of households ranked by income pay any net tax”, I say, *the data can’t be used to make statements like that*. What you *can *talk about are averages for quintiles. But *even if* you accept his ranking methodology and *even if *you assume that net tax increases with income, you *can’t* say how many households pay net tax just by looking at quintile averages.

Thanks for the more rigorous mathematics being applied to this. It rather puts Professor Richard Holden, a Professor of Economics at a prestigious Australian university no less, to shame in its analysis of the data rather than cherry picking to suite.