We all know that increasing the diversity of your boardroom increases the success of your company because politicians, business leaders and academics keep telling us so. No one has ever got into trouble for making this assertion and, in any case, we have the scientific evidence to prove it – in the form of four studies pumped out by management consultants McKinsey & Company over the past decade.

The first of these, Why Diversity Matters (2015), claimed, for example, that companies in the top quartile for gender diversity were 15 per cent more likely to outperform the median company in their industry, and companies in the top quartile for racial/ethnic diversity were 35 per cent more likely to outperform the median.

The idea seems to have bubbled up from nowhere to become a received wisdom

But what if diversity doesn’t really make a difference to a company’s performance? To date, McKinsey’s work has gone largely unchallenged, but a couple of economists, Jeremiah Green of Texas A&M University and John R.M. Hand of the University of North Carolina, have recently attempted to reproduce the management consultants’ claim – and say they have failed.

McKinsey didn’t publish a list of the companies whose performance was used in their studies – the 2015 version states that it used 366: 186 based in the US and Canada; 107 in Britain; 73 in Latin America. Green and Hand say the firm would not divulge those companies’ names. So what they did instead, in a study published in the online journal Econ Journal Watch, was to repeat McKinsey’s experiment on all 500 companies in the S&P 500 share index.

The difference in results was stark. McKinsey said it found that 58 per cent of companies in the top quartile for ethnic diversity outperformed the median company in their industry, compared with only 43 per cent in the bottom quartile. Taking just the US firms in the study, the power of diversity seemed even stronger – 61 per cent of those in the top quartile for diversity outperformed the median, compared with just 41 per cent in the bottom quartile.

When Green and Hand made the same calculations for the S&P 500 businesses, by contrast, they found that 54 per cent of companies in the top quartile for diversity outperformed the median, as did 51.2 per cent in the bottom quartile – a difference that is not statistically significant. In other words, they couldn’t detect any measurable effect on company performance of having diverse executives. This was true however they judged a firm’s success. They used six different criteria, such as revenue growth and return on equity, all with the same result: there was no statistical advantage in having an ethnically diverse board.

When it comes to explaining why increased diversity helps performance, McKinsey resorts to assertion. A more diverse board, it says, ‘increases employees’ satisfaction’ and ‘reduces conflicts between groups’. It ‘fosters innovation and creativity through a greater variety of problem-solving approaches, perspectives and ideas’ and ‘enhances company image’.

There is a potential risk, though, from having a recruitment policy focused on diversity. If you are going to promote the widest possible representation in terms of ethnicity, gender and so on, are you going to start blinding yourself to applicants’ other qualities, such as their ability to do the job? McKinsey does not appear to see the need to consider this fairly obvious problem.

It is a comforting idea that a diverse board will bring lots of different ideas to the boardroom table, but it rather depends on what is meant by diversity. The McKinsey study seems to define it purely in terms of an individual’s appearance. It classifies company executives into eight ethnic groups on a subjective assessment of photographs and names on corporate websites.

But does that really guarantee a variety of problem-solving approaches? You could, for instance, put together a theoretical cabinet made up of Rishi Sunak, Liz Truss, Rachel Reeves, Yvette Cooper, Lord Mandelson, Lord Heseltine, Angela Eagle, Baroness Vadera (the first woman to head a major British bank), Guardian writer Afua Hirsch, Labour MP Rushanara Ali and former Pakistan PM and international cricketer Imran Khan. That would look wonderfully diverse from an ethnic, gender and sexual orientation perspective – as well as having a wide political balance – but you would have recruited a body of people who all read philosophy, politics and economics at Oxford. There would be no representation whatsoever from the approximate 99.96 per cent of the UK adult population that does not have an Oxford degree in PPE.

McKinsey & Company has a pretty similar lack of educational diversity. Glance through the 31 members of its ‘shareholders council’, as it calls its board, and it resembles that 1980s pop video of ever-so-diverse pop stars singing ‘We Are the World’. Look a little closer at their biographies and you see that almost all of them have an MBA from a small pool of US and international universities. They are of a kind, schooled in the same ideas – one of which is a belief in the fundamental good of diversity.

If McKinsey wanted genuine diversity, it would dump a few of its MBAs and replace them with, say, a Texan redneck, an aborigine elder and a Mongolian goat-herder. That really would make for a variety of perspectives – and possibly result in considerably more interesting output than the usual platitudes pumped out by management consultants.

The idea that diversity improves a company’s performance seems to have bubbled up from nowhere to become a received wisdom in such circles – but without, it appears, much in the way of evidence to support it.