Everyone knows the gap between high and low incomes has grown. But much of what we think we know about why its happened, and what the government has been doing about it, is probably wrong.

For instance, many people imagine that the main thing governments do to reduce the gap between rich and poor is to raise much of their revenue via the most progressive tax in their arsenal, income tax. (A progressive tax takes a progressively higher_proportion_of tax from peoples income as incomes get higher.)

Sorry, that impressions wrong.

Another strongly held perception is that, if the gap between high and low-income people is growing, it must be because of something the government is doing. For instance, stages two and three of the Turnbull governments three-stage, seven-year tax plan are intended to make income tax significantly less progressive.

Sorry, its only partly true that growing inequality is caused by government policy.

Yet another misperception is that the inequality of incomes increases as each year passes.

These misunderstandings are whats so great about the Australian Bureau of Statisticspublicationlast month of its six-yearly fiscal incidence study, for 2015-16. Its the most comprehensive guide to whats been happening to income inequality and, in particular, how its been affected by government policies.

Professor Peter Whiteford, of the Australian National University, has written an excellentsummaryof the studys findings.

Redistributing wealth

The study allocates the federal and state taxes we pay between the nations eight million households, then allocates federal and state government spending to those households. (Some taxes, such as company tax, it cant attribute to households. Nor some classes of government spending, such as spending on defence and law and order. But these omissions should roughly cancel out.)

So, on one hand, the study takes account not just of income tax, but also all the other, federal and state indirect taxes, most of which are regressive they take a higher_proportion_of low incomes than high ones.

On the other hand, it takes account not just of government benefits in cash (pensions, the dole, family allowance), but also in kind - particularly healthcare (subsidised doctors and pharmaceuticals, free public hospitals, subsidised private insurance), subsidised aged care and childcare, plus pre-school, school, technical and university education.Add to shortlist

So it starts with households private income the money people earn from wages, profits, investments and superannuation payments then subtracts the taxes they pay and adds the value of government benefits they receive in cash and kind to get their final income.

Get it? The difference between a households private income and its final income is the net monetary effect of all the things federal and state governments budgets do to the households budget.

It shows the extent to which government budgets_redistribute_income between high and low-income households.

Before we get to that, however, note that most economists believe the_fundamental_cause of rising inequality is changes in private incomes arising from globalisation and skill-biased technological change which, over many years, have caused the wages of high-skilled workers to grow much faster than those of low-skilled workers.

Government budgets are highly effective at transferring income from the top 40 per cent of households to the bottom 40 per cent.

But the usual way to measure inequality is to compare not individual workers, but individual households, many of which contain two workers, plus dependent children.

It seems likely that, over the decades, the growing gap between high and low wages has been offset by the growing incidence of two-income families.

And note this: in more recent times the six years between 2003-04 and 2009-10 theres been no increase in inequality.

Turning back to the effect of government budgets, the study shows they redistribute a lot more income than many people realise.

Final income multiplies for the poorest

Get this: In 2015-16, the poorest 20 per cent of households (mainly pensioners) started with private income averaging just $168 week but, after taking account of their pensions and health and aged care benefits, their final income almost quintupled to $808 a week.

At the other end of the spectrum, the best-off 20 per cent of households (mainly two-income couples with good jobs) started with private income averaging $2863 a week, but had that cut to final income of $2168 a week, a loss of almost $700 a week.

How come? Well, on average they paid $714 a week in income tax and $178 in other taxes, but received just $16 in social security benefits and $192 in non-cash benefits, mainly school education.

Look now at the_middle_20 per cent of households and, on average, their final income was only a little different from their private income because the taxes they paid were pretty much offset by the benefits in cash and kind (particularly education) they received.

See whats happening? Government budgets are highly effective at transferring income from the top 40 per cent of households to the bottom 40 per cent.

It’s not just taxes doing the trick

And its not just progressive taxation that does this. Surprisingly, most of its done on the spending side of the budget.

The most common way of measuring inequality is the gini coefficient, where zero represents perfect equality between households and 100 represents one household getting all the income.

The study shows a quite high coefficient of 44.2 for private income being reduced to 24.9 for final income.

Now get this. Of this overall decline in inequality of 19.3 points, the progressive income tax scale explains only 4.5 points. And the regressive effect of other taxes reduces this by 0.8 points.

So the remaining 15.6 points of decline in inequality are explained by 8.1 points coming from governments cash social security payments, plus 7.5 points coming from the effect of governments benefits in kind, particularly health and aged care and education spending.

The first bit should be no surprise. As Whiteford reminds us, Australias system of social security payments is the most heavily means-tested in the world.

The big surprise is that our generally non-means-tested benefits-in-kind should do so much to reduce inequality.

My guess is that the high proportion of health and aged care benefits going to age pensioners does much to explain this.

Ross Gittins is economics editor of the SMH and an economic columnist for The Age. His books include_Gittins’ Guide to Economics, Gittinomics_and_The Happy Economist_.