Take income inequality in the UK, which tends to be the default metric for economic inequality. Everybody knows that it’s been rising in recent years, right? Wrong.

A recent study from the Institute for Fiscal Studies confirmed that the main measure (the Gini coefficient) has been flat for the past quarter century.

The ONS version of the same stat suggests it has actually fallen recently and is now around its lowest level since 1987. Yes, there was a big jump in income inequality in the 1980s, but there is no evidence of “rising” income inequality over recent years. In fact, the level has barely changed since Cher’s Shoop Shoop (It’s In His Kiss) was Number 1.

Faced with these facts, some jump to new metrics and try to shift the goal posts. “Ah,” they say, “but what really matters is the income share of the top one per cent!”

It’s not entirely clearly why, but here they point to data from Thomas Piketty’s World Inequality Database, which suggests that the income share of this group has indeed risen from 5.9 per cent in 1979 to 13.9 per cent in 2014.

But even this measure has been pretty much unchanged since 2000. And recent academic work has suggested that changes to corporate taxes since the 1970s may have exaggerated the perception of the jump in the income share of the top one per cent in the interim anyway.

“Okay, but it’s not income inequality that really matters, but wealth inequality,” the shapeshifting egalitarians move to, as if this will produce a different picture.

But again, the Gini coefficient measuring wealth inequality has been flat as a pancake since 2006 when the ONS started measuring it.

Yes, wealth is more unequally distributed than income, as one would expect given life‐​cycle effects and as seen across other countries.

During the period since 2006, certain components of it, not least property wealth, have become more unevenly distributed too, which is hardly surprising given the disastrous price impact of our land use planning laws mixed with rising demand.

The key point though is that overall wealth inequality just isn’t rising. In fact, wealth inequality is low by historical standards.

Looking at the wealth share of the top 10 per cent and top one per cent, it peaked around 1914, and then fell substantially through to the 1970s. Though there is some academic dispute about movements since then, the consensus is that it has either risen very modestly or remained essentially stable since the 1980s.

In other words, levels of wealth inequality are neither unprecedented nor exploding. In fact, they’d look a whole lot lower if implicit wealth entitlements, such as the state pension and healthcare promises by government, were included.

Though international comparisons are difficult across countries due to data limitations, previous research by Credit Suisse has put the UK relatively low in a wealth inequality league table too.

What about the global inequality that Corbyn lectured the UN on? Again, the Labour leader appears to know a lot that ain’t so. Research by the economist Branko Milanovic shows that overall income inequality fell between 1988 and 2008 for the first time since the Industrial Revolution, as China and India saw soaring economic growth rates.

Now, I’d argue that none of this really matters. Inequality statistics give you a snapshot of an income or wealth distribution at a point in time, telling you nothing about living standards, the fluid nature of the population, or indeed the underlying factors which have contributed to it.

These stats appear to be a particularly bad indication of wellbeing. Only Communism, mass‐​mobilisation wars, violent revolutions, and bubonic plagues appear to have narrowed income gaps greatly throughout history. In the UK, inequality fell after the financial crisis. In China, it rose due to the economic take‐​off.

But if the likes of Corbyn are going to put inequality front and centre of their political offering, they need to be honest about the facts.